the generalization of equal peak method for delay coupled nonlinear system abstract the equal peak property based extension method to a delay coupled nonlinear system is studied in this paper a time delayed vibration absorber is proposed to realize the equal peak property for a nonlinear primary system firstly the mechanical model of the nonlinear primary system coupled with the time delayed vibration absorber is established and the optimization objective is proposed then four conditions to figure out the optimum delay coupled parameters for the equal peak property with the minimum resonance peak are carried out finally several case studies with different nonlinear terms are given the results show that the equal peak property can be realized by appropriate delay coupled parameters obtained by the optimization procedure besides by selecting the optimum delay coupled parameters the two resonance peaks can be suppressed to the minimum level the design for the time delayed vibration absorber by the proposed extension method can solve the bottleneck techniques for equal peak property in nonlinear primary systems under a wide range of excitation amplitude which are concerned in manufacturing and aerospace

the beginning of the fucik spectrum for the p laplacian has a nontrivial solution u here 1 p 2p u div u p 2 u u max u 0 u uu in 1 1 denoting by 1 2 the first two eigenvalues of 2p on w 1 p 0 0 cf the end of this introduction 7p clearly contains in particular 1 1 2 2 and the two lines 1 r and r 1 this generalized notion of spectrum was introduced for p 2 i e in the linear case in the 1970s by fuc ik 21 and dancer 15 in connection article id jdeq 1999 3645 available online at http www idealibrary com on

residue harmonic balance solution procedure to nonlinear delay differential systems abstract this paper develops the residue harmonic balance solution procedure to predict the bifurcated periodic solutions of some autonomous delay differential systems at and after hopf bifurcation in this solution procedure the zeroth order solution employs just one fourier term the unbalanced residues due to fourier truncation are considered by solving linear equation iteratively to improve the accuracy the number of fourier terms is increased automatically the well known sunflower equation and van der pol equation with unit delay are given as numerical examples their solutions are verified for a wide range of system parameters comparison with those available shows that the residue harmonic balance method is effective to solve the autonomous delay differential equations moreover the present method works not only in determining the amplitude but also the frequency at bifurcation

nonresonance conditions for asymptotically positively homogeneous differential systems the fucik spectrum and its generalization in this article we propose how to define the fucik spectra for differential systems in rnwith jumping nonlinearities the propertyp a generalization of the non fucik spectra to positively homogeneous nonautonomous differential systems is also defined in the most general setting a quantitative estimate result concerning the parameterized completely continuous positively homogeneous perturbations of the identity in banach spaces is given in this article such a result is a generalization of one property in the spectrum theory for completely continuous linear operators using this estimate result we will give some significantly improved nonresonance results from the fucik spectra and propertypfor asymptotically positively homogeneous differential systems

strongly nonlinear multivalued boundary value problems in this paper we study nonlinear second order differential inclusions involving the differential operator depending on both unknown function x and its derivative x a multivalued maximal monotone operator and nonlinear multivalued boundary conditions our framework is general and can be applied to the classical boundary value problems namely the dirichlet the neumann and the periodic problems using notions and techniques from the nonlinear operator theory and from multivalued analysis we obtain solutions for both the convex and nonconvex problems finally we present the cases of special interest which fit into our framework illustrating the generality of our results

time delay effects on coupled limit cycle oscillators at hopf bifurcation abstract we present a detailed study of the effect of time delay on the collective dynamics of coupled limit cycle oscillators at hopf bifurcation for a simple model consisting of just two oscillators with a time delayed coupling the bifurcation diagram obtained by numerical and analytical solutions shows significant changes in the stability boundaries of the amplitude death phase locked and incoherent regions a novel result is the occurrence of amplitude death even in the absence of a frequency mismatch between the two oscillators similar results are obtained for an array of n oscillators with a delayed mean field coupling and the regions of such amplitude death in the parameter space of the coupling strength and time delay are quantified some general analytic results for the n thermodynamic limit are also obtained and the implications of the time delay effects for physical applications are discussed

amplitude and kinematic corrections of migrated images for nonunitary imaging operators obtaining migrated images with meaningful amplitudes is a challenging problem when the migration operator is not unitary one possible solution to this problem is iterative inversion however inversion is an expensive process that can be rather difficult to apply especially with 3d data in this paper i propose estimating migrated images similar to the least squares inverse images by approximating the inverse hessian thus avoiding the need for iterative inversion the inverse hessian is approximated with a bank of nonstationary matching filters these filters are not exact impulse responses and are limited in their ability to mimic the full effects of least squares inversion tests on two data sets show that this filtering approach gives results similar to iterative least squares inversion at a lower cost this technique is flexible enough to be applied to images migrated from zero offset or angle domain common image point gathers

an efficient method for switching branches of period doubling bifurcations of strongly non linear autonomous oscillators with many degrees of freedom abstract popular algorithms for switching branches at a bifurcation point of strongly non linear oscillators are generally quite involved as they require the computation of the tangent of a new branch and second derivatives in this paper a simple but efficient algorithm is presented by using a perturbation incremental method for switching branches at a period doubling bifurcation of strongly non linear autonomous oscillators with many degrees of freedom to switch to a new branch at a bifurcation point a parameter is simply turned on from zero to a small positive value so as to obtain an initial solution on the emanating branch for subsequent continuation the parametric value at a period doubling bifurcation can also be determined accurately furthermore limit cycles of period 2 k k 1 can be calculated to any desired degree of accuracy

generalization of fredholm alternative for nonlinear differential operators on considere le probleme aux valeurs limites u t p 2 u t f t u t g t t 0 u 0 u 0 on demontre que si lim u inf f t u u p 2 u lim u sup f t u u p 2 u sont entre des valeurs propres du probleme aux valeurs propres u p 2 u u p 2 u sur 0 u 0 u 0 alors le probleme aux limites est resoluble pour tout g l 1

bifurcation analysis in active control system with time delay feedback in this study a model of active control system with time delay feedback is investigated and time delays were set in control loop an efficient method was used to analyze the stability of the system by solving the characteristic equation the local stability and the existence of codimension one bifurcation hopf bifurcation and fold bifurcation were obtained regarding the time delay as bifurcation parameters the direction of the hopf bifurcation and the stability of bifurcation periodic solution by applying the normal form theory and center manifold theorem numerical simulations were also given to illustrate the results obtained

synchronization based topology identification of weighted general complex dynamical networks with time varying coupling delay abstract many existing papers investigated the geometric features control and synchronization of complex dynamical networks provided with certain topology however the exact topology of a network is sometimes unknown or uncertain based on lasalle s invariance principle we propose an adaptive feedback technique to identify the exact topology of a weighted general complex dynamical network model with time varying coupling delay by receiving the network nodes evolution the topology of such a kind of network with identical or different nodes or even with varying topology can be monitored in comparison with previous methods time delay is taken into account in this simple analytical and systematic synchronization based technique particularly the weight configuration matrix is not necessarily symmetric or irreducible and the inner coupling matrix need not be symmetric illustrative simulations are provided to verify the correctness and effectiveness of the proposed scheme

splitting of operators alternate directions and paraxial approximations for the three dimensional wave equation we design a family of new three dimensional 3 d paraxial equations well adapted to numerical solution by the alternate directions method these equations do not suffer from bad anisotropic effects and the cost for their numerical integration remains cheap in comparison with classical paraxial equations

transition from anticipatory to lag synchronization via complete synchronization in time delay systems the existence of anticipatory complete and lag synchronization in a single system having two different time delays that is feedback delay tau1 and coupling delay tau2 is identified the transition from anticipatory to complete synchronization and from complete to lag synchronization as a function of coupling delay tau2 with a suitable stability condition is discussed in particular it is shown that the stability condition is independent of the delay times tau1 and tau2 consequently for a fixed set of parameters all the three types of synchronizations can be realized further the emergence of exact anticipatory complete or lag synchronization from the desynchronized state via approximate synchronization when one of the system parameters b2 is varied is characterized by a minimum of the similarity function and the transition from on off intermittency via periodic structure in the laminar phase distribution

periodic solutions for van der pol equation with time delay for van der pol equation with distributed delay when the distributed delay kernel is the general gamma distributed delay kernel the existence and the stability of periodic solution are obtained by using the linear chain trick and geometric singular perturbation theory on the other hand for van der pol equation with discrete delay the existence and the stability are proved by employing a technique which is based on inertial manifold finally numerical simulations are also given to illustrate the results

inversion of seismic reflection data in the acoustic approximation the nonlinear inverse problem for seismic reflection data is solved in the acoustic approximation the method is based on the generalized least squares criterion and it can handle errors in the data set and a priori information on the model multiply reflected energy is naturally taken into account as well as refracted energy or surface waves the inverse problem can be solved using an iterative algorithm which gives at each iteration updated values of bulk modulus density and time source function each step of the iterative algorithm essentially consists of a forward propagation of the actual sources in the current model and a forward propagation backward in time of the data residuals the correlation at each point of the space of the two fields thus obtained yields the corrections of the bulk modulus and density models this shows in particular that the general solution of the inverse problem can be attained by methods strongly related to the methods of migration of unstacked data and commerc

fast 2 d ray born migration inversion in complex media in this paper we evaluate the capacity of a fast 2 d ray born migration inversion algorithm to recover the true amplitude of the model parameters in 2 d complex media the method is based on a quasi newtonian linearized inversion of the scattered wavefield asymptotic green s functions are computed in a smooth reference model with a dynamic ray tracing based on the wavefront construction method the model is described by velocity perturbations associated with diffractor points both the first traveltime and the strongest arrivals can be inverted the algorithm is implemented with several numerical approximations such as interpolations and aperture limitation around common midpoints to speed the algorithm both theoritical and numerical aspects of the algorithm are assessed with three synthetic and real data examples including the 2 d marmousi example comparison between logs extracted from the exact marmousi perturbation model and the computed images shows that the amplitude of the velocity perturbations

sturm type problems for singular p laplacian boundary value problems in this paper the eigenvalue problem of singular p laplacian boundary value problems is discussed which is a generalization of the classical sturmian theorem for second order ordinary differential equations as an application the existence of solutions to singular boundary value problem is discussed

stability and bifurcations of equilibria in a multiple delayed differential equation the influence of multiple negative delayed feedback loops on the stability of a single action mechanism are considered a characteristic equation for the linearized stability of the equilibrium is completely analyzed as a function of two parameters describing a delay in one loop and a ratio of the gains in the two feedback loops the bifurcations occurring as the linear stability is lost are analyzed by the construction of a centre manifold in particular the nature of hopf and more degenerate higher codimension bifurcations are explicitly determined

on the resonance problem with nonlinearity which has arbitrary linear growth abstract this paper deals with the nonlinear two point boundary value problem at resonance even nonlinearities g with an arbitrary linear growth in resp may be considered but only on the cost of the corresponding bound on their linear growth at resp it generalizes the previous results in this direction obtained by m schechter j shapiro and m snow trans amer math soc 241 1978 69 78 l cesari and r kannan proc amer math soc 88 1983 605 613 and s ahmad proc amer math soc 93 1984 381 384

delay induced instabilities in nonlinear feedback systems extending general methods developed in synergetics to construct order parameter equations we work out a systematic elimination procedure for the stable modes in nonlinear delay systems it will be shown that in the vicinity of an instability the dynamical behavior of the infinite dimensional delay system is approximately governed by a low dimensional set of order parameter equations which turn out to be of the form of ordinary differential equations i e they no longer contain memory terms the general formalism will then be compared with experimental data obtained from the nonlinear operation of a phase locked loop where the finite propagation time of the signal in the feedback loop is taken into account

limit cycle oscillators subject to a delayed feedback the coexistence of two stable limit cycles exhibiting different periods is examined for a nonlinear oscillator subject to a delayed feedback for the case of a weakly nonlinear oscillator we discuss the validity of a previously determined phase equation for the case of a strongly nonlinear oscillator we derive a phase equation and analyze its bifurcation diagram our analysis is motivated by previous experimental studies of chemical oscillators controlled by a delayed feedback

modified imaging principle an alternative to preserved amplitude least squares wave equation migration impedance contrast images can result from a least squares migration or from a modified imaging principle theoretically the two approaches should give similar results but in practice they lead to different estimates of the impedance contrasts because of limited acquisition geometry difficulty in computing exact weights for least squares migration and small contrast approximation to analyze those differences we compare the two approaches based on 2d synthetics forward modeling is either a finite difference solver of the full acoustic wave equation or a one way wave equation solver that correctly models the amplitudes the modified imaging principle provides better amplitude estimates of the impedance contrasts and does not suffer from the artifacts at tributable to diving waves which can be seen in two way least squares migrated sections however because of the shot based formulation artifacts appear in the modified imaging principle results in shadow zones where energy is defocused those artif

3 d implicit finite difference migration by multiway splitting we show that 3 d implicit finite difference schemes can be realized by multiway splitting in such a way that the steep dip problem and the problem of numerical anisotropy are overcome the basic idea is as follows we approximate the 3 d square root operator by a sequence of 2 d operators in three four or six directions to solve the azimuth symmetry problem each 2 d square root operator is then approximated by a sequence of implicit 2 d operators to improve steep dip accuracy this sequence contains some unknown coefficients which are calculated by a taylor expansion technique or by an optimization technique in the taylor expansion method the square root and its approximation are expanded into power series by comparing the terms the unknown coefficients are calculated the more 2 d finite difference operators for cascading are taken and the more directions for downward continuation are chosen the more terms from power series can be compared to obtain a higher degree migration operator with better

hopf pitchfork bifurcation in van der pol s oscillator with nonlinear delayed feedback abstract first we identify the critical values for hopf pitchfork bifurcation second we derive the normal forms up to third order and their unfolding with original parameters in the system near the bifurcation point by the normal form method and center manifold theory then we give a complete bifurcation diagram for original parameters of the system and obtain complete classifications of dynamics for the system furthermore we find some interesting phenomena such as the coexistence of two asymptotically stable states two stable periodic orbits and two attractive quasi periodic motions which are verified both theoretically and numerically

zero hopf bifurcation for van der pol s oscillator with delayed feedback in this paper we study the dynamical behaviors of the following van der pol oscillator with delay x e x 2 1 x x eg x t t in the case that its associated characteristic equation has a simple zero root and a pair of purely imaginary roots zero hopf singularity the normal form is obtained by performing a center manifold reduction and by using the normal form theory developed by faria and magalhaes a critical value e 0 of e in 0 2 is obtained to predict the bifurcation diagrams from which saddle node bifurcation pitchfork bifurcation hopf bifurcation the existence and stability of the periodic solutions and heteroclinic bifurcation are determined some examples are given to confirm the theoretical results

the response of a duffing van der pol oscillator under delayed feedback control abstract the nonlinear dynamics of a duffing van der pol oscillator under linear plus nonlinear state feedback control with a time delay are investigated by means of the averaging method and taylor expansion two slow flow equations for the amplitude and phase of the primary resonance response are derived from which the relations between the amplitude and phase of the primary resonance response and all other parameters are obtained respectively the singularity analysis of the equation governing the amplitude of the primary resonance response shows that the bifurcation modes are perturbations of the pitchfork bifurcation conditions preventing multiple solutions corresponding to two different kinds of bifurcation modes are given since cases for which multiple solutions are available should be avoided the stable condition for steady state response is also given by the routh hurwitz criterion it is also shown that coupled nonlinear state feedback control can be replaced by uncoupled nonlinear state feedback control

nonlinear boundary value problems for second order differential inclusions abstract in this paper we study a class of nonlinear value boundary problems for second order differential inclusions with nonlinear perturbations which satisfy the generalized hartman condition weaker than that considered in some papers using techniques from multivalued analysis theory of monotone operators and fixed points we prove the existence of solutions in both convex and nonconvex cases our framework can be incorporated with dirichlet neumann and mixed boundary problems

a homotopic deformation along p of a leray schauder degree result and existence for u p 2u ƒ t u 0 u 0 u t 0 p 1 soit f 0 1 r r une fonction continue et soit o p r r definie par o p s s p 2 s pour p fixe 1 on considere le probleme de dirichlet suivant o p u f t u 0 u 0 u t 0 ou t est un nombre reel positif

p laplacian problems with jumping nonlinearities we consider the p laplacian boundary value problem 1 p u x f x u x u x a e x 0 1 2 c00u 0 c01u 0 c10u 1 c11u 1 where p 1 is a fixed number p s s p 2s s r and for each j 0 1 cj0 cj1 0 the function f 0 1 r2 r is a caratheodory function satisfying for x s t 0 1 r2 x p s e x s t f x s t x p s e x s t s 0 where l1 0 1 and e has the form e x s t x e s t with l1 0 1 0 e 0 and limr e r r1 p 0 this condition allows the nonlinearity in 1 to behave differently as u such a nonlinearity is often termed jumping related to 1 2 is the problem 3 p u a p u b p u p u in 0 1 together with 2 where a b l1 0 1 r and u x max u x 0 for x 0 1 this problem is positively homogeneous and jumping values of for which 2 3 has a nontrivial solution u will be called half eigenvalues while the corresponding solutions u will be called half eigenfunctions we show that a sequence of half eigenvalues exists the corresponding half eigenfunctions having certain nodal properties and we obtain certain spectral and degree theoretic properties of the set of half eigenvalues these properties lead to existence and nonexistence results for the problem 1 2 we also consider a related bifurcation problem and obtain a global bifurcation result similar to the well known rabinowitz global bifurcation theorem this then leads to a multiplicity result for 1 2 when the functions a and b are constant the set of half eigenvalues is closely related to the fucik spectrum of the problem and equivalent solvability results are obtained using the two approaches however when a and b are not constant the half eigenvalue approach yields stronger results

dynamics of a limit cycle oscillator under time delayed linear and nonlinear feedbacks abstract we study the effects of time delayed linear and nonlinear feedbacks on the dynamics of a single hopf bifurcation oscillator our numerical and analytic investigations reveal a host of complex temporal phenomena such as phase slips frequency suppression multiple periodic states and chaos such phenomena are frequently observed in the collective behavior of a large number of coupled limit cycle oscillators our time delayed feedback model offers a simple paradigm for obtaining and investigating these temporal states in a single oscillator we construct a detailed bifurcation diagram of the oscillator as a function of the time delay parameter and the driving strengths of the feedback terms we find some new states in the presence of the quadratic nonlinear feedback term with interesting characteristics like birhythmicity phase reversals radial trapping phase jumps and spiraling patterns in the amplitude space our results may find useful applications in physical chemical or biological systems

least squares wave equation migration for avp ava inversion we present an acoustic migration inversion algorithm that uses extended double square root wave equation migration and modeling operators to minimize a constrained least squares data misfit function least squares migration we employ an imaging principle that allows for the extraction of ray parameter domain common image gathers cigs from the propagated seismic wavefield the cigs exhibit amplitude variations as a function of half offset ray parameter avp closely related to the amplitude variation with reflection angle ava our least squares wave equation migration inversion is constrained by a smoothing regularization along the ray parameter this approach is based on the idea that rapid amplitude changes or discontinuities along the ray parameter axis result from noise incomplete wavefield sampling and numerical operator artifacts these discontinuities should therefore be penalized in the inversion the performance of the proposed algorithm is examined with two synthetic examples in the first

first passage failure of a business cycle model under time delayed feedback control and wide band random excitation abstract first passage failure of a classical business cycle model subject to time delayed feedback control and wide band random excitation is investigated in this paper first we get the averaged equation by using a stochastic averaging method and then a backward kolmogorov equation governing the conditional reliability function and a set of generalized pontryagin equations governing the conditional moments of first passage time are established the conditional reliability function the conditional probability density and moments of first passage time are obtained by solving the backward kolmogorov equation and generalized pontryagin equations analytically and numerically with suitable initial and boundary conditions the results show that time delay in the feedback control forces may remarkably reduce the conditional reliability and the mean first passage time of the controlled economics system

a van der pol mathieu equation for the dynamics of dust grain charge in dusty plasmas the chaotic profile of dust grain dynamics associated with dust acoustic oscillations in a dusty plasma is considered the collective behaviour of the dust plasma component is described via a multi fluid model comprising boltzmann distributed electrons and ions as well as an equation of continuity possessing a source term for the dust grains the dust momentum and poisson s equations a van der pol mathieu type nonlinear ordinary differential equation for the dust grain density dynamics is derived the dynamical system is cast into an autonomous form by employing an averaging method critical stability boundaries for a particular trivial solution of the governing equation with varying parameters are specified the equation is analysed to determine the resonance region and finally numerically solved by using a fourth order runge kutta method the presence of chaotic limit cycles is pointed out

delay and periodicity systems with time delay play an important role in modeling of many physical and biological processes in this paper we describe generic properties of systems with time delay which are related to the appearance and stability of periodic solutions in particular we show that delay systems generically have families of periodic solutions which are reappearing for infinitely many delay times as delay increases the solution families overlap leading to increasing coexistence of multiple stable as well as unstable solutions we also consider stability issue of periodic solutions with large delay by explaining asymptotic properties of the spectrum of characteristic multipliers we show that the spectrum of multipliers can be split into two parts pseudocontinuous and strongly unstable the pseudocontinuous part of the spectrum mediates destabilization of periodic solutions

an open plus closed loop opcl control of complex dynamic systems a new method of contmlfing arbitrary nonlinear dynamic systems dx dt f x t x c n is presented it is proved that there exists solutions x t in the neighborhood of any arbitrary goal dynamics g t that are entrained to g t through the use of an additive controlling action k g x t h dg dt g c g t g t x which is the sum of the openloop h ibler action h dg dt g and a suitable linear closed lo0p feedback action c g t examples of some newly obtained entrainment capabilities are given for the during and van der pol systems for these and the lorenz and rtssler systems proofs are given for global basins of entrainment for all goal dynamics that can be exponentially bounded in time the basin of entrainment is also established for the chua system as well as the possibility of a coexisting basin of attraction to another fixed point

outer synchronization between two nonidentical networks with circumstance noise abstract this paper regards the outer synchronization between two delay coupled complex dynamical networks with nonidentical topological structures and a noise perturbation considering one network as the drive network and the other one as the response network the drive response system achieves synchronous states through a suitably designed adaptive controller the stochastic lasalle invariance principle is employed to theoretically prove the almost sure synchronization between two networks finally two numerical examples are examined in order to illustrate the proposed synchronization scheme

strongly nonlinear second order differential inclusions with generalized boundary conditions abstract in this paper we study second order differential inclusions in r n with a maximal monotone term and generalized boundary conditions the nonlinear differential operator need not be necessary homogeneous and incorporates as a special case the one dimensional p laplacian the generalized boundary conditions incorporate as special cases well known problems such as the dirichlet picard neumann and periodic problems as application to the proven results we obtain existence theorems for both convex and nonconvex problems when the maximal monotone term a is defined everywhere and when not case of variational inequalities

adaptive backstepping synchronization between chaotic systems with unknown lipschitz constant abstract the error between two nonlinear terms is a key point of many synchronization problems however the lipschitz constant of the nonlinear term is not always easy to calculate for the stability analysis of the controlled error system thus the nonlinear systems with unknown parameters and unknown lipschitz constant is considered in this paper their scalar synchronous controller is proposed based on the thought of backstepping design without the need to evaluate the invariant set and calculate the lipschitz constant an assistant adaptive estimator is designed for the lipschitz constant what s more as a problem solving skill two different estimators are used on the same unknown parameter finally the synchronization control for both chaotic autonomous van der pol duffing advp systems and chaotic genesio systems with unknown parameters are given as examples to verify the control effect

robust stability for interval hopfield neural networks with time delay the conventional hopfield neural network with time delay is intervalized to consider the bounded effect of deviation of network parameters and perturbations yielding a novel interval dynamic hopfield neural network idhnn model a sufficient condition related to the existence of unique equilibrium point and its robust stability is derived

numerical hopf bifurcation for a class of delay differential equations abstract in this paper we consider discretization of parameter dependent delay differential equations of the form x t f x t x t r we show that if the delay differential equation undergoes a hopf bifurcation then the discrete scheme undergoes a hopf bifurcation of the same type the results of this paper extend the results of our previous analysis relating to the discretization of the delay logistic equation to a wider class of problems

effects of time delayed position feedback on a van der pol duffing oscillator abstract the mechanism for the action of time delay in a non autonomous system is investigated in this paper the original mathematical model under consideration is a van der pol duffing oscillator with excitation a delayed system is obtained by adding both linear and nonlinear time delayed position feedbacks to the original system functional analysis is used to change the delayed system into a functional differential equation fde the time delay is taken as a variable parameter to investigate its effect on the dynamics of the system such as the stability and bifurcation of an equilibrium point phase locked periodic and phase shifting solution period doubling quasi periodic motion and chaos a periodic solution expressed in the closed form with the aid of the center manifold and averaging theorem is found to be in good agreement with that obtained by numerical simulation two routes to chaos are found namely period doubling bifurcation and torus breaking the results obtained in this paper show that time delay may be used as a simple but efficient switch to control motions of a system either from order motion to chaos or from chaotic motion to order for different applications

nonuniform nonresonance of semilinear differential equations abstract consider the dirichlet problem of nonlinear differential equations with the principal part the p laplacian when the nonlinearity satisfies some semilinearity conditions the usual nonuniform nonresonance conditions are obtained by comparing nonlinear equations with the classical eigenvalues in this article we will introduce some weighted eigenvalues the nonuniform nonresonance conditions proved in this article using weighted eigenvalues will improve the usual ones significantly

existence and nonexistence of solutions for quasilinear elliptic equations abstract in this paper we study the problem p u f x u u in u 0 on where r n is a smooth bounded domain n 2 and p u div u p 2 u defines the p laplacian we provide some necessary and sufficient conditions on f under which the problem admits a weak solution for the case p 2 we obtain more general conditions on f the main ingredients are degree theory and the super subsolution method

periodic problems for strongly nonlinear second order differential inclusions in this paper we study periodic problems for second order differential inclusions in rn with a maximal monotone term the nonlinear differential operator is not necessarily homogeneous does not obey any growth condition and incorporates as a special case the one dimensional p laplacian using techniques from multivalued analysis and the theory of operators of monotone type we prove the existence of solutions for both the convex and nonconvex problems when the maximal monotone term a is defined everywhere and when it is not defined everywhere case of variational inequalities

on a pseudo fuccik spectrum for strongly nonlinear second order odes and an existence result abstract we study here the existence of solutions to the nonlinear dirichlet problem p u f t u q t a e for t a b u a u b 0 where is an increasing odd homeomorphism of r f a b r r satisfies the caratheodory assumptions and q l 1 a b r with a view towards defining a pseudo fucik spectrum pfs we study using a time mapping approach the eigenvalue like problem u a u b u 0 u a 0 u b where a 0 b 0 we show here that this pfs which we denote by l consists of a set of curves in r 2 resembling the classical fucik spectrum i e when s s our main existence result which deals with nonresonance with respect to the pfs can be roughly stated as follows if for s 0 sufficiently large and for almost every t a b the pair f t s s f t s s lies in a compact rectangle contained in an open component of r 2 l which intersects the diagonal then problem p has at least a solution

delay induced dynamics of an axially moving string with direct time delayed velocity feedback abstract the local dynamics of an axially moving string under aerodynamic forces is investigated with a time delayed velocity feedback controller the retarded differential difference governing equation is obtained in modal coordinates of a two degree of freedom system through galerkin s discretization procedure the stability of trivial equilibrium is examined with the change of counting multiplicity of eigenvalue with positive real part the hopf bifurcation curves are determined in the controlling parameter spaces with the aid of the center manifold reduction a functional analysis is carried out to reduce the modal equation to a single ordinary differential equation of one complex variable on the center manifold the approximate analytical solutions in the vicinity of hopf bifurcations are derived in the case of primary resonance the curves of excitation response and frequency response curves are shown with the effect of time delay the stability analysis for steady state periodic solutions of the reduced system indicates the onset of local control parameter for vibration control and response suppression moreover the poincare bendixson theorem and energy considerations are used to investigate the existences and characteristics of quasi periodic solutions when stability of the periodic solution is lost numerical results demonstrate the validity of the analytical prediction two different kinds of quasi periodic solutions are found