uniform boundedness of conditional gauge and schrodinger equations we prove that for a bounded domaind rn withc2 boundary and q in k n loc n geqq 3 if e x exp int limits 0 tau d q x t dt mathop ddag limits infty ind then mathop sup limits mathop x in d limits z in partial d e z x exp int limits 0 tau d q x t dt infty xt brownian motion

remarks about a generalized pseudo relativistic hartree equation abstract with appropriate hypotheses on the nonlinearity f we prove the existence of a ground state solution u for the problem m 2 u v u w f u f u in r n where 0 1 v is a bounded continuous potential and f the primitive of f we also show results about the regularity of any solution of this problem

an efficient algorithm for the multivariable adomian polynomials abstract in this article the sum of the series of multivariable adomian polynomials is demonstrated to be identical to a rearrangement of the multivariable taylor expansion of an analytic function of the decomposition series of solutions u 1 u 2 u m about the initial solution components u 1 0 u 2 0 u m 0 of course the multivariable adomian polynomials were developed and are eminently practical for the solution of coupled nonlinear differential equations the index matrices and their simplified forms of the multivariable adomian polynomials are introduced we obtain the recurrence relations for the simplified index matrices which provide a convenient algorithm for rapid generation of the multivariable adomian polynomials another alternative algorithm for term recurrence is established in these algorithms recurrence processes do not require complicated operations such as parametrization expanding and regrouping derivatives etc as practiced in prior art the mathematica program generating the adomian polynomials based on the algorithm in this article is designed

nonlinear elliptic equations related to weighted sum operators abstract we study a new kind of degenerate operators related to some weighted sum operators although the operators are severely degenerate we show the smoothness of the weak solutions

local behavior of solutions of quasilinear elliptic equations with general structure this paper is motivated by the observation that solutions to certain variational inequalities involving partial differential operators of the form diva x u vu b x u vu where a and b are borel measurable are solutions to the equation diva x u vu b x u vu u for some nonnegative radon measure i among other things it is shown that if u is a holder continuous solution to this equation then the measure u satisfies the growth property j b x r 1 is given by the structure of the differential operator conversely if u is assumed to satisfy this growth condition then it is shown that u satisfies a harnack type inequality thus proving that u is locally bounded under the additional assumption that a is strongly monotonic it is shown that u is holder continuous

normal forms for periodic systems the theory of normal forms for autonomous differential equations based on the lie bracket has proved to be an important technique in determining the behaviour of solutions of nonlinear differential equations near a stationary solution it has been widely used in the bifurcation theory for autonomous ordinary differential equations see e g 1 3 6 9 11 i in its simplest form the theory applies to an equation of the form

a recursive approach to compute normal forms normal forms are instrumental in the analysis of dynamical systems described by ordinary differential equations particularly when singularities close to a bifurcation are to be characterized however the computation of a normal form up to an arbitrary order is numerically hard this paper focuses on the computer programming of some recursive formulas developed earlier to compute higher order normal forms a computer program to reduce the system to its normal form on a center manifold is developed using the maple symbolic language however it should be stressed that the program relies essentially on recursive numerical computations while symbolic calculations are used only for minor tasks some strategies are proposed to save computation time examples are presented to illustrate the application of the program to obtain high order normalization or to handle systems with large dimension

on the failure of static stability analyses of nonconservative systems in regions of divergence instability abstract the stability of perfect bifurcational discrete dissipative systems under follower loads in regions of existence non existence of adjacent equilibria is thoroughly re examined in the light of recent progress in nonlinear dynamics a general theory for such nongradient systems described by autonomous ordinary differential equations is developed conditions for the existence of adjacent equilibria the stability of precritical critical and postcritical states as well as for different types of local bifurcations are established focusing attention on the interaction of geometric nonlinearities and vanishing damping new findings contradicting widely accepted results of the classical linear analysis are discovered in a small region of adjacent equilibria near a compound branching point which is explicitly determined an interaction of two consecutive postbuckling modes occurs related to the following phenomena in case of vanishing damping loss of stability may occur via a hopf dynamic bifurcation prior to static divergence buckling moreover the critical states of divergence instability may be associated with a double zero jacobian eigenvalue satisfying also the conditions of a hopf local bifurcation besides local dynamic bifurcations global bifurcations are also found an example is used to illustrate the qualitative findings

elliptic equations strongly degenerate at a point abstract in this paper we will mainly propose some problems for a class of degenerate elliptic equations either linear or nonlinear we will study some special cases of these problems and reveal some phenomena which may not have been noticed previously our problems originated from the self similar solutions of the heat flow of harmonic maps we will prove that the self similar solutions or the so called quasi harmonic spheres are discontinuous at infinity for the equivariant case in other words the equivariant quasi harmonic spheres are not continuous images of topological spheres

harnack s inequality for degenerate schrodinger operators on etablit une inegalite d harnack pour les solutions faibles non negatives de certaines equations de schrodinger de la forme lu vu 0 ou l est un operateur elliptique degenere du second ordre sous forme de divergence et v un potentiel d une certaine classe

on codimension three bifurcations in the motion of articulated tubes conveying a fluid abstract we consider the planar motion of two articulated tubes conveying a fluid near a double degeneracy in the linearized dynamical equations in particular the interaction between hopf and pitchfork symmetric saddle node bifurcations and the effects of asymmetries on that interaction are studied in detail the fourth order system of nonlinear equations is reduced to a third order system using center manifold theory the method of averaging provides the normal form which can be considered as a planar vector field with three important parameters one each for the hopf bifurcation the pitchfork bifurcation and the asymmetry this second order system is shown to possess twenty three open sets in the parameter space each with qualitatively different phase portraits some of these portraits are presented along with bifurcation analysis and the physical implications of the results are discussed

global and chaotic dynamics for a parametrically excited thin plate the global bifurcations and chaotic dynamics of a parametrically excited simply supported rectangular thin plate are analyzed the formulas of the thin plate are derived by von karman type equation and galerkin s approach the method of multiple scales is used to obtain the averaged equations based on the averaged equations theory of normal form is used to give the explicit expressions of normal form associated with a double zero and a pair of pure imaginary eigenvalues by maple program on the basis of the normal form global bifurcation analysis of the parametrically excited rectangular thin plate is given by a global perturbation method developed by kovacic and wiggins the chaotic motion of thin plate is found by numerical simulation

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

the limited effectiveness of normal forms a critical review and extension of local bifurcation studies of the brusselator pde abstract the detection and unfolding of degenerate local bifuractions provides one of very few generally applicable analytical tools for studying complex dynamics in systems of arbitrarily high dimension using the brusselator partial differential equations pdes prigogine and lefever 1968 as motivation and main example we critically review this method we extend and correct previous calculations presenting explicit formulae from which normal forms accurate to third order may be computed and for the first time we carefully compare bifurcations and dynamics of these normal forms with those of the untransformed systems restricted to a center manifold and with galerkin and finite difference approximations of the original pde while judicious use of symbolic manipulations makes feasible such high order center manifold and normal form calculations we show that the conclusions drawn from them are of limited use in understanding spatio temporal complexity and chaos as guckenheimer 1981 argued the method permits proof of existence of quasi periodic motions and under mild genericity assumptions sil nikov chaos sub shifts of finite type but the parameter and phase space ranges in which these results may be applied are extremely small

regularity for a class of strongly degenerate quasilinear operators abstract we prove a harnack inequality and regularity for solutions of a quasilinear strongly degenerate elliptic equation we assume the coefficients of the structure conditions to belong to suitable stummel kato classes

conditional gauge with unbounded potential let b be a ball in r d and q be a borel function on it we prove that if mathtype mtef 2 1 feaafiart1ev1aaatcvaufebsjuyzl2yd9gzlbvynv2caerbulwbln hiov2dgi1btfmbaexatlxbi9gbaerbd9wdylwzybitldharqqtubsr 4rnchbgeagqivu0je9sqqrpepc0xbbl8f4rqqrffpeea0xe9gqpe0 rq0dxdd9vqaq jfrvkfhe9pgea0dxdar jb9hs0dxdbpyxe9vr0 vr 0 vqpwqaaeaabigaciaacaqabeaadaqaaqaaaoqaamaaxababagaci 4caiaacwhacaggwbaaleaacawg4bgaeyici4sabmoqayaaraaabeaa ieaakiaa bcadawdrbqaamaalaaabagaaiifaiaadghacaggoagaam yeaiaacmcacagg8baabagaaiifaiaadihacqghsislcawg5bgaaiif amaacaaaleqabagaamizaiabgkhitiaaikdaaaaaaogaa8hiagqaci aa rgacagf5baaleaacawgcbaabeqdcqghrii8aaaa 4fb6 mathop sup limits x in bar b int limits b frac q y x y d 2 dy is sma11 enough then mathtype mtef 2 1 feaafiart1ev1aaatcvaufebsjuyzl2yd9gzlbvynv2caerbulwbln hiov2dgi1btfmbaexatlxbi9gbaerbd9wdylwzybitldharqqtubsr 4rnchbgeagqivu0je9sqqrpepc0xbbl8f4rqqrffpeea0xe9gqpe0 rq0dxdd9vqaq jfrvkfhe9pgea0dxdar jb9hs0dxdbpyxe9vr0 vr 0 vqpwqaaeaabigaciaacaqabeaadaqaaqaaaoqaamaaxababagaci 4caiaacwhacaggwbaaleaadawfqaqaaiaadihacqghiiizcawgcbaa meaacawg6bgaeyici4saeyoaiyraamoqaaqabaaaleqaagqaaogaa8 hiagqaciaa veadaqhaawcbagaa4neaaqaaiaa hhaaagcdawadaqa aigacwgacagg4bgaaiicaiaa bcadawdxbqaaiaa fhacawfoagaa4 heamaabaaaleaacagf0baabeaakiaacmcacawgkbgaamidaawcbaga a8hmaaqaaiaadshadawgaaadbagaamoqaaqabaaaniabguiiydaaki aawufacagldbaacawfgagaa8hpaiaa bcacawfragaa8hiaiabg6hi lcaa 5a6b mathop sup limits mathop x in b limits z in partial b e z x left exp int limits 0 t b q x t dt right infty this paper gives a new proof of one of the two main results by aizenman and simon in 1 by a simple and elementary method a basic theorem in chung and rao 2 is extended to the class of q treated in 1

harnack inequality and regularity for degenerate quasilinear elliptic equations we prove harnack inequality and local regularity results for weak solutions of a quasilinear degenerate equation in divergence form under natural growth conditions the degeneracy is given by a suitable power of a strong a weight regularity results are achieved under minimal assumptions on the coefficients and as an application we prove c1 local estimates for solutions of a degenerate equation in non divergence form

static and dynamic local and global bifurcations in nonlinear autonomous structural systems discrete damped or undamped gradient systems described by nonlinear autonomous ordinary differential equations ode of motion are examined in detail emphasis is given to the relationship between static with possibly existing dynamic bifurcations criteria for dynamic bifurcations and stability of precritical critical and postcritical states associated with the nature of jacobian eigenvalues are also presented cases of discrepancies between local and global dynamic analysis regarding the stability of equilibriums are reported for the first time finally using a simple energy criterion exact dynamic buckling loads for vanishing but nonzero damping are readily obtained

liouville theorems for quasi harmonic functions abstract let n be a compact riemannian manifold a self similar solution for the heat flow is a harmonic map from r n e x 2 2 n 2 d s 0 2 to n n 3 which was also called a quasi harmonic sphere cf lin and wang 1999 1 here d s 0 2 is the euclidean metric in r n it arises from the blow up analysis of the heat flow at a singular point when n r and without the energy constraint we call this a quasi harmonic function in this paper we prove that there is neither a nonconstant positive quasi harmonic function nor a nonconstant l p r n e x 2 2 n 2 d s 0 2 p n n 2 quasi harmonic function however for all 1 p n n 2 there exists a nonconstant quasi harmonic function in l p r n e x 2 2 n 2 d s 0 2

on characterization of poisson integrals of schrodinger operators with bmo traces abstract let l be a schrodinger operator of the form l v acting on l 2 r n where the nonnegative potential v belongs to the reverse holder class b q for some q n let bmo l r n denote the bmo space on r n associated to the schrodinger operator l in this article we will show that a function f bmo l r n is the trace of the solution of l u u t t l u 0 u x 0 f x where u satisfies a carleson condition sup x b r b r b n 0 r b b x b r b t u x t 2 d x d t c conversely this carleson condition characterizes all the l harmonic functions whose traces belong to the space bmo l r n this result extends the analogous characterization founded by fabes johnson and neri in 13 for the classical bmo space of john and nirenberg

harnack principle for weakly coupled elliptic systems abstract we prove the harnack inequality for the weakly coupled elliptic system s where su big begin align l 1 cdots l n end align big u qu and u big begin align u 1 cdot cdot cdot u n end align big l k k 1 n are second order elliptic operators with holder continuous coefficients and q is a matrix valued function with singular entries in the case that q is irreducible a full harnack principle is proved

a perturbation analysis of interactive static and dynamic bifurcations the instability behavior of a nonlinear autonomous system in the vicinity of a coincident critical point which leads to interactions between static and dynamic bifurcations is studied the critical point considered is characterized by a simple zero and a pair of pure imaginary eigenvalues of the jacobian and the system contains two independent parameters the static and dynamic bifurcations and quasiperiodic motions resulting from the interaction of the bifurcation modes and the associated invariant tori are analyzed by a novel unification technique that is based on an intrinsic perturbation procedure divergence boundary dynamic bifurcation boundary secondary bifurcations and invariant tori are determined explicitly two illustrative examples concerning control systems are presented

holder continuity for solutions of linear degenerate elliptic equations under minimal assumptions abstract in this paper we study the local regularity of solutions to linear degenerate elliptic equations of the form i j 1 n a ij u x i d j u x j i 1 n b i u x i cu f i 1 n f i x i we prove harnack s inequality for positive solutions and the holder continuity of the solutions of assuming on the coefficients of the lower order terms very general hypotheses involving appropriate degenerate morrey spaces

center manifolds normal forms and bifurcations of vector fields with application to coupling between periodic and steady motions abstract we study the instabilities known to aeronautical engineers as flutter and divergence mathematically these states correspond to bifurcations to limit cycles and multiple equilibrium points in a differential equation making use of the center manifold and normal form theorems we concentrate on the situation in which flutter and divergence become coupled and show that there are essentially two ways in which this is likely to occur in the first case the system can be reduced to an essential model which takes the form of a single degree of freedom nonlinear oscillator this system which may be analyzed by conventional phase plane techniques captures all the qualitative features of the full system we discuss the reduction and show how the nonlinear terms may be simplified and put into normal form invariant manifold theory and the normal form theorem play a major role in this work and this paper serves as an introduction to their application in mechanics repeating the approach in the second case we show that the essential model is now three dimensional and that far more complex behavior is possible including nonperiodic and chaotic motions throughout we take a two degree of freedom system as an example but the general methods are applicable to multi and even infinite degree of freedom problems

criteria for occurrence of flutter instability before buckling the occurrence of utter instability through a hopf bifurcation before static buckling in regions of divergence in nonconservative nonself adjoint dissipative systems is thoroughly discussed using a qualitative analysis this region where both ziegler s and static criterion may fail to predict the actual critical load is de ned via two values bounds of the nonconservativenessloadingparameter the upperboundcorresponds to 0 5 being invariant with respect to all other parameters whereas the lower bound corresponds to a double critical divergence point beyond which there are no adjacent equilibria the location of the last point lying always between 0 and 0 5 depends on a stiffness parameter it is also found that the region of nonexistence of adjacent equilibria becomes maximum minimum when the double critical point corresponds to 0 5 0 the interaction of vanishing damping with various parameters leads to new phenomena related to point and periodic attractors as well as to a new type of dynamic bifurcation

singularity and regularity of solutions to a certain class of degenerate elliptic equations abstract in this note we consider the solution of the degenerate elliptic system 1 div f x u 0 x b 1 0 u b 1 c b 1 where b 1 denotes the unit ball in r n and f is smooth and increasing on 0 1 with f 0 0 f r 0 r 0 it is known that there exists a unique solution u c b 1 0 l b 1 to this elliptic system here we will study the property of u at the origin at first we give the necessary and sufficient condition such that u can be extended to a continuous function in b furthermore we also give the necessary and sufficient condition such that u is a holder continuous function in b 1

sensitivities and linear stability analysis around a double zero eigenvalue a general multiparameter system admitting a double zero eigenvalue at a critical equilibrium point is considered a sensitivity analysis of the critical eigenvalues is performed to explore the neighborhood of the critical point in the parameter space because the coalescence of the eigenvalues implies that the jacobian matrix is defective or nilpotent well suited techniques of perturbation analysis must be employed to evaluate the eigenvalues and the eigenvector sensitivities different asymptotic methods are used based on perturbations both of the eigenvalue problem and the characteristic equation the analysis reveals the existence of a generic nonsingular case and of a nongeneric singular case however even in the generic case a codimension 1 subspace exists in the parameter space on which a singularity occurs by the use of the relevant asymptotic expansions linear stability diagrams arebuiltup and different bifurcation mechanisms divergence hopf doubledivergence doubledivergence hopf degeneratehopf arehighlighted the problem of e nding a uniqueexpression uniformly valid in the wholespaceis then addressed it isfound that a second degreealgebraic equation governsthebehaviorofthecriticaleigenvalues it also permits clarie cation of the geometrical meaning of the unfolding parameters which has been discussed in literature for the takens bogdanova bifurcation finally a mechanical system loaded by nonconservative forces and exhibiting a double zero bifurcation is studied as an example

a compactness result for fano manifolds and kahler ricci flows we obtain a compactness result for fano manifolds and kahler ricci flows comparing to the more general riemannian versions in anderson invent math 102 2 429 445 1990 and hamilton am j math 117 545 572 1995 in this fano case the curvature assumption is much weaker and is preserved by the kahler ricci flows one assumption is the c 1 boundedness of the ricci potential and the other is the smallness of perelman s entropy as one application we obtain a new local regularity criteria and structure result for kahler ricci flows the proof is based on a holder estimate for the gradient of harmonic functions and mixed derivative of green s function

a study of the limit cycles associated with a generalized codimension 3 lienard oscillator in this paper melnikov and petrov methods are used to study the limit cycles associated with the degenerate bifurcations of a representative generalized codimension 3 lienard oscillator it is shown that the coexistence of multiple limit cycles is possible and that jumping phenomena exist between limit cycles moreover it is found that the stable limit cycles oscillations and the unstable limit cycles oscillations can occur alternatively

analytical solution of the bagley torvik equation by adomian decomposition method abstract the fractional derivative has been occurring in many physical problems such as frequency dependent damping behavior of materials motion of a large thin plate in a newtonian fluid creep and relaxation functions for viscoelastic materials the pi d controller for the control of dynamical systems etc phenomena in electromagnetics acoustics viscoelasticity electrochemistry and material science are also described by differential equations of fractional order the solution of the differential equation containing fractional derivative is much involved instead of application of the existing methods an attempt has been made in the present analysis to obtain the solution of bagley torvik equation r l bagley p j torvik on the appearance of the fractional derivative in the behavior of real materials asme j appl mech 51 1984 294 298 i podlubny fractional differential equations academic press san diego ca usa 1999 by the relatively new adomian decomposition method the results obtained by this method are then graphically represented and then compared with those available in the work of podlubny i podlubny fractional differential equations academic press san diego ca usa 1999 a good agreement of the results is observed

on schrodinger operators with multipolar inverse square potentials abstract positivity essential self adjointness and spectral properties of a class of schrodinger operators with multipolar inverse square potentials are discussed in particular a necessary and sufficient condition on the masses of singularities for the existence of at least a configuration of poles ensuring the positivity of the associated quadratic form is established

new ideas for proving convergence of decomposition methods in this paper we give new formulae which calculate easily the adomian s polynomials used in decomposition methods then the proof of convergence of the adomian s technique becomes almost obvious by using a weak hypothesis on the nonlinear operator of the functional equation

blow up and global existence for heat flows of harmonic maps in this paper it is proved that the solution to the evolution problem for harmonic maps blows up in finite time if the initial map belongs to some nontrivial homotopy class and the initial energy is sufficiently small

regularity for quasilinear degenerate elliptic equations equations like 1 1 have been studied by many authors in the case x 1 see e g 2 and the references therein or an a2 muckenhoupt weight 6 and 17 here 3 is a strong a weight and 31 p n 1 p n the novelty here is the degeneracy condition given by choice of the weight to be a power of a strong a weight moreover we assume very mild integrability conditions on the lower order terms and known term in 1 1 these conditions are sharp and at least in some instances are necessary and sufficient see e g 5 or 12 the non degenerate case was studied in 16 and 15 our main result is contained in theorem 4 3 and it states the harnack inequality for nonnegative weak solutions of equation 1 1 as a direct consequence smoothness for weak solutions is obtained in particular we have continuity result under stummel kato type assumptions and holder continuity result under morrey type assumptions see theorems 5 1 and 5 2 we will prove our results using as main tool a weighted fefferman poincare embedding see theorem 3 2 mixed with the moser iteration technique this investigation was suggested by b franchi and we thank him for enlightening discussions about strong a weights we also thank the anonymous referee for very good suggestions to improve the presentation and l saloff coste for useful discussions

a numerical solution of the sine gordon equation using the modified decomposition method the decomposition method for solving the sine gordon equation has been implemented by using a number of initial values the explicit and numerical solutions of the equation are calculated in the form of convergent power series with easily computable components the present method performs extremely well in terms of accuracy efficiency simplicity stability and reliability

green function for schrodinger operator and conditioned feynman kac gauge consider the schrodinger operator h 2 q in a bounded c1 1 domain d with q klocd d q satisfies the condition sup spec 2 q d v x y g x y e y x exp 0 t q x t d t x y d where xt is the conditioned brownian motion starting at x and ending at y with the life time t and v g can be extended to a continuous and positive function on d d specifically we give the comparison theorem there exists a constant c c d q 0 such that 1 c g x y v x y c g x y x y d another result is that v nz x z x d z d exists and represents the poisson kernel for the dirichlet problem corresponding to schrodinger operator h

holder regularity for non divergence form elliptic equations with discontinuous coefficients abstract in this note we study the global holder regularity for the gradient of the strong solutions of non variational elliptic equations

imperfection sensitivity of interacting hopf and steady state bifurcations and their classification abstract the bifurcation problem of interacting time periodic and stationary solutions of nonlinear evolution equations with double degeneracy is discussed in terms of singularity and imperfect bifurcation theory a complete classification up to symmetry covariant contact equivalence and codimension three of generic perturbations of interacting hopf and steady state bifurcations is presented the sensitivity of the bifurcation diagrams to imperfections is analyzed normal forms describing sequences of secondary and tertiary bifurcations leading to motions on tori are determined a variety of phenomena such as gaps in hopf branches periodic motions not stably connected to steady states and the formation of islands is discovered which one can expect to find in perturbed evolution equations on pure geometric grounds implications for physical systems are discussed

convergence of adomian s method applied to differential equations this paper deals with a new proof of convergence of adomian s method applied to differential equations we also give new formulae and properties and we suggest a simple computational form for adomian s polynomials

the restrictions and improvement of the adomian decomposition method the adomian decomposition method is a creative and effective method for exactly solving functional equations of various kinds in this paper the principle of the decomposition method is described and its restrictions are discussed then an improvement is proposed which overcomes the restrictions and complements the ability of the adomian decomposition method some concrete examples are also studied to illustrate the validity of the improvement

keller osserman a priori estimates and the harnack inequality for the evolution p laplace equation with singular absorption term abstract in this paper we study quasilinear equations of type u t d i v u p 2 u v x f u 0 p 2 u 0 despite the lack of comparison principle we prove a priori estimates of keller osserman type using these estimates we give a proof of the intrinsic harnack inequality

instability of lightly damped linear nonconservative systems in computing the critical load for a linear nonconservative system one needs to construct the load frequency curve from the characteristic equation that contains asymmetric matrices based on the finite element formulation traditionally this requires repeated solution of complex eigenvalues from the characteristic equation at many load levels which is extremely time consuming in practice small damping of the rayleigh type is assumed a bieigenvalue curve is adopted to approximate the load frequency curve for the first few modes of interest such a curve can be uniquely determined once the derivatives of the frequency with respect to the load parameter have been calculated for a preset load level after the bieigenvalue curve is established the critical load can be computed by setting its first derivative equal to zero the effectiveness of the present method is demonstrated in the numerical study

comparison of the solutions obtained by adomian decomposition and wavelet galerkin methods of boundary value problems abstract in this paper we will compare the performance of adomian decomposition method and the wavelet galerkin method applied to the solution of boundary value problems involving non homogeneous heat and wave equations it is shown that the adomian decomposition method in many instances gives better results in the wavelet galerkin solutions daubechies six wavelets are used because they give better results than those of lower degree wavelets the results are then compared with those obtained using the adomian decomposition method although the adomian decomposition solution required slightly more computational effort than the wavelet galerkin solution it resulted in more accurate results than the wavelet galerkin method

solving a multi order fractional differential equation using adomian decomposition abstract an algorithm has been developed to convert the multi order fractional differential equation d y t f t y t d 1 y t d n y t y k 0 c k k 0 m where m d denotes caputo fractional derivative of order into a system of fractional differential equations further adomian decomposition method has been employed to solve the system of fractional differential equations some illustrative examples are presented

a numerical simulation and explicit solutions of the generalized burgers fisher equation we consider solitary wave solutions of the generalized burgers fisher bf equation u t pu ru x u x x qu 1 u r 0 in this paper by considering the decomposition scheme we first obtain the exact solutions of the generalized bf equation for the initial condition without using any classical transformations and then its numerical solutions are constructed without using any discretization technique the numerical solutions are compared with the known analytical solutions its remarkable accuracy is finally demonstrated in the study of some values r 2 of the generalized bf equation

reconstruction of material losses by perimeter penalization and phase field methods abstract we treat the inverse problem of determining material losses such as cavities in a conducting body by performing electrostatic measurements at the boundary we develop a numerical approach based on variational methods to reconstruct the unknown material loss by a single boundary measurement of current and voltage type the method is based on the use of phase field functions to model the material losses and on a perimeter like penalization to regularize the otherwise ill posed problem we justify the proposed approach by a convergence result as the error on the measurement goes to zero

harnack inequality and continuity of weak solutions for doubly degenerate elliptic equations we prove harnack inequality and regularity for solutions of a quasilinear doubly degenerate elliptic equation generated by grushin vector fields we assume the coefficients of the structure conditions to belong to suitable stummel kato classes

holder continuity of weak solutions of a class of linear equations with boundary degeneracy abstract this paper deals with a class of linear equations with boundary degeneracy according to the degenerate ratio the equations are divided into weakly degenerate ones and strongly degenerate ones which should be supplemented by different dirichlet boundary value conditions after establishing some necessary existence nonexistence and comparison principles we investigate the optimal holder continuity of weak solutions in these two cases utilizing the harnack inequality and the morrey theorem respectively

applications of extended tanh method to special types of nonlinear equations in this paper we explore more applications of extended tanh method to some special nonlinear equations such equations are not of differential polynomial form so that cannot be directly dealt with by tanh method or extended tanh method as examples we apply a recently proposed extended tanh method to build some new explicit solutions for 2 1 dimensional sine gordon equation dodd bullough mikhailov equation and coupled schrodinger kdv equation

evolutionary weighted p laplacian with boundary degeneracy abstract the paper concerns the well posedness problem of an evolutionary weighted p laplacian with boundary degeneracy different from the classical theory for linear equations it is shown that the degenerate portion of the boundary should be decomposed into two parts the strongly degenerate boundary on which the equation exhibits hyperbolic characteristics and the weakly degenerate boundary on which the equation still exhibits parabolic characteristics we formulate reasonably the boundary value condition and establish the existence and uniqueness theorems

bifurcation analysis of double pendulum with a follower force abstract the stability and bifurcations of a double pendulum with a follower force are considered the focus is placed on a doubly degenerate system which possesses a zero eigenvalue and a pair of pure imaginary eigenvalues that is coupled flutter and divergence bifurcation the local qualitative behavior of the system is examined in the neighborhood of the degenerate system the four dimensional equations of motion are reduced to the two dimensional ones by using some qualitative reduction theory for dynamical systems and it is shown that two distinct bifurcations can occur in the system according to the ratio of two damping coefficients of the double pendulum numerical simulations have been performed using the original four dimensional equations to confirm the analytical results some global forms of behavior of the solutions have also been investigated numerically

an application of the modified decomposition method for two dimensional sine gordon equation in this study the decomposition method for solving two dimensional sine gordon equation has been implemented by using a number of initial values the explicit and numerical solutions of the equation are calculated the present method performs extremely well in terms of numerical accuracy and efficiency

homoclinic tangencies in the dynamics of articulated pipes conveying fluid abstract numerical evidence is presented showing homoclinic tangencies to periodic orbits occuring in a four dimensional system of ordinary differential equations that describes the dynamics of a pair of articulated pipes conveying fluid bifurcation sequences of mixed mode oscillations are discovered in two separate regions of parameter space in one region the equations have z 2 symmetry and a symmetric pair of heteroclinic tangencies is implied in both cases satisfactory agreement is found between the observed bifurcation sequences and the local theory of homoclinic tangencies global branches of mixed mode orbits are computed it is discovered that some orbits are generated by either sil nikov or figure of eight homoclinic orbits to stationary points whereas others form isolas that feature characteristic towers of saddle node and period doubling bifurcations

adomian decomposition method for solution of nonlinear differential algebraic equations in m m hosseini adomian decomposition method with chebyshev polynomials appl math comput in press an efficient modification of the adomian decomposition method was presented by using chebyshev polynomials also in m m hosseini adomian decomposition method for solution of differential algebraic equations j comput appl math in press solution of linear differential algebraic equations was considered by adomian decomposition method in this paper standard and modified adomian decomposition methods are applied to non linear differential algebraic equations the schemes are tested for some examples and the results demonstrate reliability and efficiency of the proposed methods

global stabilty analysis of a classical non conservative system under a follower load abstract the bifurcations critical conditions and global stability of the classical two degree of freedom ziegler s dissipative model under a partial follower load are thoroughly discussed with the aid of a complete non linear dynamic analysis attention is mainly focused on the range of values of the non conservativeness loading parameter for which adjacent equilibria do not exist various characteristic findings are established by studying the nature of the jacobian matrix eigenvalues associated with the above non linear autonomous dissipative system it is found that the system exhibits stable hopf bifurcations global stability for the entire region of non adjacent equilibria while the classical linear stability analysis leads to flutter instability local instability moreover in an explicit general form the significant effect of damping on the critical dynamic bifurcation load is established on the basis of the latter the critical loads for the case of vanishing damping are found to be completely different from those of the classical local stability analysis all findings of this analysis are checked against numerical solution of the equations of motion

eigenfunctions for quasi laplacian abstract to study the regularity of heat flow lin and wang 1999 introduced the quasi harmonic sphere which is a harmonic map from m r m e x 2 2 m 2 d s 0 2 to n with finite energy here d s 0 2 is euclidean metric in r m ding and yongqiang 2006 showed that if the target is a sphere any equivariant quasi harmonic spheres is discontinuous at infinity the metric g e x 2 2 m 2 d s 0 2 is quite singular at infinity and it is not complete in this paper we mainly study the eigenfunction of quasi laplacian g e x 2 2 m 2 g 0 g 0 h g 0 e x 2 2 m 2 h for h x 2 4 in particular we show that there are infinite number of eigenvalues of the quasi laplacian g of which the corresponding eigenfunctions are discontinuous at and any non constant eigenfunction of drifted laplacian h g 0 g 0 h g 0 is discontinuous at infinity

bifurcations and chaotic motions in the autonomous system of a restrained pipe conveying fluid the stability and dynamics of a cantilevered pipe conveying fluid with motion limiting constraints and a linear spring support have been investigated emphasis is placed on analyzing local qualitative behavior of the system in the neighborhood of a doubly degenerate point using some qualitative reduction methods of dynamical system theory the four dimensional differential equation of motion is reduced to a two dimensional one and then the possible motions of the pipe are predicted through analyzing bifurcations of the solution to the reduced equation of motion the unfolding result is found to be in good agreement with the result obtained using the numerical method it is also found that there exist the quasi periodic motions and route to chaos through breakup of the quasi periodic torus surface in some parameter region of the system which differs from that of periodic doubling bifurcation route found earlier in this system numerical simulations have been performed using the four dimensional equation of motion to confirm the analytical results

flow induced bifurcations to three dimensional oscillatory motions in continuous tubes three dimensional motions of a cantilever tube carrying an incompressible fluid and having rotational symmetry about the vertical axis are examined for bifurcating oscillatory solutions the system behavior depends on two parameters rho the flow velocity and beta the mass ratio of the fluid and the tube as the flow rate is increased past a critical value the zero solution becomes unstable by a double pair of complex conjugate eigenvalues of the linearized operator crossing the imaginary axis using ideas from the center manifold theory and the method of integral averaging the governing partial differential equations are reduced to a set of four nonlinear ordinary differential equations it is then shown that the system bifurcates into two qualitatively distinct oscillatory motions these oscillatory solutions themselves for some values of the mass ratio beta bifurcate into more complex amplitude modulated oscillations

criteria for occurrence of flutter instability before buckling in nonconservative dissipative systems the occurrence of flutter instability through a hopf bifurcation before static buckling in regions of divergence in nonconservative nonself adjoint dissipative systems is thoroughly discussed using a qualitative analysis this region where both ziegler s and static criterion may fail to predict the actual critical load is defined via two values bounds of the nonconservativeness loading parameter the upper bound corresponds to 0 5 being invariant with respect to all other parameters whereas the lower bound corresponds to a double critical divergence point beyond which there are no adjacent equilibria the location of the last point lying always between 0 and 0 5 depends on a stiffness parameter it is also found that the region of nonexistence of adjacent equilibria becomes maximum minimum when the double critical point corresponds to 0 5 0 the interaction of vanishing damping with various parameters leads to new phenomena related to point and periodic attractors as well as to a new type of dynamic bifurcation

a reliable modification of adomian decomposition method in this paper we propose a powerful modification of adomian decomposition method that will accelerate the rapid convergence of the series solution the validity of the modified technique is verified through illustrative examples in all cases of differential and integral equations we obtained excellent performance from the modified algorithm the modification could lead to a promising approach for many applications in applied sciences

local birth of homoclinic chaos abstract local generation of chaotic behaviours associated with a sil nikov homoclinic orbit is studied near the codimension two bifurcation at the double stationary oscillatory instability of eigenvalues 0 we develop a perturbative calculation of the sil nikov homoclinic orbit and of its bifurcation locus starting from a conservative vector field flat nonanalytic behaviours due to non axisymmetric perturbations of the normal form are discussed and we show that the codimension one locus of sil nikov homoclinicity is unavoidable near bicriticality under certain conditions the results are applied to rossler s model quasiperiodic regimes born at the double instability are also studied and illustrated in the rossler model

harnack inequality and smoothness for quasilinear degenerate elliptic equations we prove local and global regularity for the positive solutions of a quasilinear variational degenerate equation assuming minimal hypothesis on the coefficients of the lower order terms as an application we obtain holder continuity for the gradient of solutions to nonvariational quasilinear equations

bifurcations in a two degree of freedom elastic system with follower forces abstract the stability and bifurcations of a two degree of freedom elastic system subjected to follower forces are studied attention is mainly concentrated on local behavior small amplitude motions about a centre equilibrium for the parameter values in the neighborhood of some point on the stability boundaries by using centre manifold theory and some codimension two bifurcations it is shown that a number of distinct bifurcations may occur in such a system according to the ratio of two damping coefficients numerical integrations of the full equations of motion have been performed to confirm the analytical aspects of the local solutions as well as to understand some aspects of the global behavior of the solutions

finite element solution of the stability problem for nonlinear undamped and damped systems under nonconservative loading a nonlinear finite element analysis of elastic structures which can be studied by a 3d beam theory subjected to conservative as well as to nonconservative forces is presented the stability behaviour of the system is studied by means of an eigenvalue analysis the stiffness matrix of the eigenvalue problem is asymmetric i e non self adjoint system the flutter and divergence modes of instability as well as the values of the critical load are identified for a number of numerical examples belonging to the benchmark tests proposed by nafems 1990 the results demonstrate the reliability of this finite element formulation in particular the effect of damping on the stability behaviour of such structures is investigated and the destabilizing effect of small damping is underlined finally the need to define a number of benchmark tests for nonlinear nonconservative analyses in presence of damping is included

lie transformations nonlinear evolution equations and painleve forms we present the results of a systematic investigation of invariance properties of a large class of nonlinear evolution equations under a one parameter continuous lie group of transformations it is shown that in general the corresponding invariant variables the subclass of which is the usual similarity variables lead to ordinary differential equations of painleve type in the case of inverse scattering transform solvable equations as conjectured by ablowitz ramani and segur this is found to be also true for certain higher spatial dimensional versions such as the kadomtsev petviashivilli two dimensional sine gordon and ernst equations for the nonsolvable equations considered here this invariance study leads to ordinary differential equations with movable critical points

bifurcations associated with a double zero and a pair of pure imaginary eigenvalues interactive static and dynamic bifurcations associated with a nonlinear autonomous system and the stability properties of various solutions are explored attention is focused on the vicinity of a compound critical point where the jacobian of the system exhibits a double zero eigenvalue of index one and a pair of pure imaginary eigenvalues the system under consideration has three independent parameters and depending on the route followed in the parameter space the system may exhibit static bifurcations hopf bifurcations secondary hopf bifurcations and bifurcations into two or three dimensional tori the general analysis is based on a perturbation method which combines an intrinsic harmonic balancing technique with a certain unification procedure this approach leads to bifurcation equations and simplified differential equations governing the local dynamics in the vicinity of the compound critical point a control system is analyzed for illustration

singularities of first kind in the harmonic map and yang mills heat flows by constructing examples which are explicit up to solving an ode we prove that singularities of first kind exist for the harmonic map and yang mills heat flows as a by product we also get a simplified proof of ratto s ding s theorem about the existence of harmonic hopf constructions

the existence of regions of divergence instability for nonconservative systems under follower forces abstract in this investigation the existence of regions of divergence instability for an elastically restrained column under a follower compressive force at its end is discussed necessary and sufficient conditions for the existence of regions of divergence instability are established the boundary between flutter and divergence instability passes always through a double critical point where the first and second static buckling eigenmodes coincide the eigenvalues buckling loads of nonself adjoint problems of this type are positive and distinct for the entire region of divergence instability except at its boundary where the first and second eigenvalues coincide at this boundary where the buckling mechanism changes from divergence to flutter and vice versa a sudden increase in the critical load occurs with the flutter load always being higher than the corresponding divergence load

modal analysis of mechanical systems with impact non linearities limitations to a modal superposition this paper presents an attempt to generalize the modal superposition formula to mechanical systems with impact type non linearities following the procedure introduced for smooth non linearities the study is restricted to simple one and two degree of freedom systems with a unilateral constraint on one of the degrees of freedom for which the response can be analytically determined generalized frequencies modes and masses are built in the procedure the results obtained for various sets of parameters point out some limitations to the validity of a general modal superposition formula