emden fowler equations involving critical exponents on considere le probleme y t k y 2 y 2k 3 0 t 0 pour t 2 0 0 soit t inf t 0 y 0 sur t alors t 0 0 on etudie comment la position t du premier zero de y t varie avec

asymptotic behaviour of finite energy solutions of polyharmonic equations asymptotic behaviour of solutions of polyharmonic equations on exterior domains in r n is considered under suitable conditions on f it is shown that finite energysolutions u have the asymptotic property this partially extends results of egnell 6 for m 1

multiple and sign changing solutions for a class of semilinear biharmonic equation abstract in this paper under an improved hardy rellich s inequality we study the existence of multiple and sign changing solutions for a biharmonic equation in unbounded domain by the minimax method and linking theorem

renormalization proof for spontaneously broken yang mills theory with flow equations in this paper we present a renormalizability proof for spontaneously broken su 2 gauge theory it is based on flow equations i e on the wilson renormalization group adapted to perturbation theory the power counting part of the proof which is conceptually and technically simple follows the same lines as that for any other renormalizable theory the main difficulty stems from the fact that the regularization violates gauge invariance we prove that there exists a class of renormalization conditions such that the renormalized green functions satisfy the slavnov taylor identities of su 2 yang mills theory on which the gauge invariance of the renormalized theory is based

a meshless method for solving the cauchy problem in three dimensional elastostatics the application of the method of fundamental solutions to the cauchy problem in three dimensional isotropic linear elasticity is investigated the resulting system of linear algebraic equations is ill conditioned and therefore its solution is regularized by employing the first order tikhonov functional while the choice of the regularization parameter is based on the l curve method numerical results are presented for both under and equally determined cauchy problems in a piece wise smooth geometry the convergence accuracy and stability of the method with respect to increasing the number of source points and the distance between the source points and the boundary of the solution domain and decreasing the amount of noise added into the input data respectively are analysed

on singular q curvature type equations this paper is devoted to q curvature type equations with singularities mainly we give existence and regularity results of solutions to have positive solutions which will be meaningful in conformal geometry we restrict ourself to special manifolds

extremal functions and best constants to an inequality involving hardy potential and critical sobolev exponent abstract in this paper we study the asymptotic behavior of radial extremal functions to an inequality involving hardy potential and critical sobolev exponent based on the asymptotic behavior at the origin and the infinity we shall deduce a strict inequality between two best constants finally as an application of this strict inequality we consider the existence of a nontrivial solution of a quasilinear brezis nirenberg type problem with hardy potential and critical sobolev exponent

an adaptive boundary element scheme for steady thermoelastostatic analysis previously developed adaptive boundary element h refinement scheme called sample point error analysis and related mesh refinement by extended error indicator is applied to the linear and steady thermoelastic problem thermal and elastic analyses are divided into two stages for which two different methodologies for boundary element adaptation are tried difficulties in this approach are that the boundary element distribution is preferable in common for both analyses and that influence magnitudes of element error on solution inconsistencies of temperature and of displacement are taken into account individually approximate but sufficiently sound strategy is developed and applied to two dimensional examples the results prove the usefulness of the scheme

the mfs for the cauchy problem in two dimensional steady state linear thermoelasticity we study the reconstruction of the missing thermal and mechanical fields on an inaccessible part of the boundary for two dimensional linear isotropic thermoelastic materials from over prescribed noisy cauchy data on the remaining accessible boundary this problem is solved with the method of fundamental solutions mfs together with the method of particular solutions mps via the mfs based particular solution for two dimensional problems in uncoupled thermoelasticity developed in marin and karageorghis 2012a 2013 the stabilisation regularization of this inverse problem is achieved by using the tikhonov regularization method tikhonov and arsenin 1986 whilst the optimal value of the regularization parameter is selected by employing hansen s l curve method hansen 1998

on semilinear elliptic problems involving critical exponents abstract in this paper we study brezis nirenberg type results for radial solutions of a semilinear elliptic equation of the form u c x u b x u q 2 u a e x b r 0 r n r 0 u 0 on b r 0 where r q 2 and the weights b c are appropriate positive measurable radially symmetric functions

asymptotic behaviour of higher order semilinear equations equation 1 1 is said to be sublinear if 0 c y 1 and singular if 1 y 0 because of the lack of a maximum principle for higher order equations methods which have been successfully applied to equations of order 2 are not available for equation 1 l this includes most importantly the method of sub and super solutions or barriers as a consequence ordinary differential equation methods have been used and the results have generally been applicable only to radially symmetric equations in their study of the semilinear biharmonic equation

global well posedness and scattering for the focusing energy critical nonlinear schrodinger equations of fourth order in the radial case we consider the focusing energy critical nonlinear schrodinger equation of fourth order iut 2u u 8d 4u d 5 we prove that if a maximal lifespan radial solution u i rd c obeys supt i u t 2 w 2 then it is global and scatters both forward and backward in time here w denotes the ground state which is a stationary solution of the equation in particular if a solution has both energy and kinetic energy less than those of the ground state w at some point in time then the solution is global and scatters

quantization of the nonlinear sigma model revisited we revisit the subject of perturbatively quantizing the nonlinear sigma model in two dimensions from a rigorous mathematical point of view our main contribution is to make precise the cohomological problem of eliminating potential anomalies that may arise when trying to preserve symmetries under quantization the symmetries we consider are twofold i diffeomorphism covariance for a general target manifold ii a transitive group of isometries when the target manifold is a homogeneous space we show that there are no anomalies in case i and that ii is also anomaly free under additional assumptions on the target homogeneous space in agreement with the work of friedan we carry out some explicit computations for the o n model finally we show how a suitable notion of the renormalization group establishes the ricci flow as the one loop renormalization group flow of the nonlinear sigma model

existence results for brezis nirenberg problems with hardy potential and singular coefficients abstract in this paper we consider the existence of non trivial solutions to semi linear brezis nirenberg type problems with hardy potential and singular coefficients first we shall study the corresponding eigenvalue problem and obtain some basic properties of eigenvalues and asymptotic estimates of the eigenfunctions and approximating eigenfunctions secondly we consider the extremal functions of the best embedding constant and get some crucial estimates for the cut off function of the extremal functions thirdly applying different variational theorems for distinct cases of those parameters appearing in the equation we obtain two existence results for non trivial solutions to semi linear brezis nirenberg type problems our existence results are divided into non resonant and resonant cases

mayer expansions and the hamilton jacobi equation we review the derivation of wilson s differential equation in infinitely many variables which describes the infinitesimal change in an effective potential of a statistical mechanical model or quantum field theory when an infinitesimal integration out is performed we show that this equation can be solved for short times by a very elementary method when the initial data are bounded and analytic the resulting series solutions are generalizations of the mayer expansion in statistical mechanics the differential equation approach gives a remarkable identity for connected parts and precise estimates which include criteria for convergence of iterated mayer expansions applications include the yukawa gas in two dimensions past the 4 threshold and another derivation of some earlier results of gopfert and mack

an invariant method of fundamental solutions for two dimensional isotropic linear elasticity abstract in this paper we propose an invariant method of fundamental solutions for solving boundary value problems in two dimensional isotropic linear elasticity the invariant method of fundamental solutions keeps a very basic natural property the so called invariance property under trivial coordinate changes in the problem description e g dilations and or contractions the problems are solved by the tikhonov regularization method in conjunction with morozov s discrepancy principle finally five examples of boundary value problems are investigated to show the efficiency of this method the numerical convergence accuracy and stability of the proposed method with respect to the number of source points the distance between the sources and the boundary and the amount of noise added into the input data respectively are also analyzed

matrix decomposition mfs algorithms for elasticity and thermo elasticity problems in axisymmetric domains in this work we propose an efficient matrix decomposition algorithm for the method of fundamental solutions when applied to three dimensional boundary value problems governed by elliptic systems of partial differential equations in particular we consider problems arising in linear elasticity in axisymmetric domains the proposed algorithm exploits the block circulant structure of the coefficient matrices and makes use of fast fourier transforms the algorithm is also applied to problems in thermo elasticity several numerical experiments are carried out

a meshless singular boundary method for three dimensional elasticity problems summary this study documents the first attempt to extend the singular boundary method sbm a novel meshless boundary collocation method for the solution of three dimensional 3d elasticity problems the sbm involves a coupling between the regularized boundary element method bem and the method of fundamental solutions mfs the main idea here is to fully inherit the dimensionality and stability advantages of the former and the meshless and integration free attributes of the later this makes it particularly attractive for problems in complex geometries and three dimensions four benchmark 3d problems in linear elasticity are well studied to demonstrate the feasibility and accuracy of the proposed method the advantages disadvantages and potential applications of the proposed method as compared with the fem bem and mfs are also examined and discussed this article is protected by copyright all rights reserved

critical semilinear biharmonic equations in rn an existence theorem is obtained for a fourth order semilinear elliptic problem in r n involving the critical sobolev exponent n 4 n 4 n 4 a preliminary result is that the best constant in the sobolev embedding l 2n n 4 r n is attained by all translations and dilations of 1 x 2 4 n 2 the best constant is found to be

nonexistence theorems for singular solutions of quasilinear partial differential equations on etudie les etats fondamentaux singuliers de l equation de poisson semilineaire u f u 0 et de son analogue quasi lineaire div a du du f u 0 ou est le laplacien a n dimensions et a p et f u sont des fonctions donnees

the method of fundamental solutions for the cauchy problem in two dimensional linear elasticity in this paper the application of the method of fundamental solutions to the cauchy problem in two dimensional isotropic linear elasticity is investigated the resulting system of linear algebraic equations is ill conditioned and therefore its solution is regularised by employing the first order tikhonov functional while the choice of the regularisation parameter is based on the l curve method numerical results are presented for both smooth and piecewise smooth geometries as well as for constant and linear stress states the convergence and the stability of the method with respect to increasing the number of source points and the distance between the source points and the boundary of the solution domain and decreasing the amount of noise added into the input data respectively are analysed

recovery of a space dependent vector source in anisotropic thermoelastic systems abstract we investigate the theoretical and numerical determination of a space dependent vector source load in an anisotropic thermoelastic system of type iii from the knowledge of an additional final time measurement the uniqueness of a solution to this inverse source problem is proved for various assumptions made on the convolution kernel a convergent and stable iterative algorithm is proposed for the recovery of the unknown vector source in the linear case and at the same time a stopping criterion is also given three numerical experiments are considered to validate the properties of the proposed iterative procedure and the regularizing stabilizing character of the corresponding stopping criterion the numerical experiments carried out showed that it exists a certain limitation of the method with respect to the recovery of non symmetric sources

a meshless method for some inverse problems associated with the helmholtz equation in this paper a new numerical scheme based on the method of fundamental solutions is proposed for the numerical solution of some inverse boundary value problems associated with the helmholtz equation including the cauchy problem since the resulting matrix equation is badly ill conditioned a regularized solution is obtained by employing truncated singular value decomposition while the regularization parameter for the regularization method is provided by the l curve method numerical results are presented for problems on smooth and piecewise smooth domains with both exact and noisy data and the convergence and stability of the scheme are investigated these results show that the proposed scheme is highly accurate computationally efficient stable with respect to the noise in the data and convergent with respect to decreasing the amount of data noise and increasing the distance between the physical and fictitious boundaries and could be considered as a competitive alternative to existing methods for these problems

a meshless method for the numerical solution of the cauchy problem associated with three dimensional helmholtz type equations in this paper the application of the method of fundamental solutions to the cauchy problem associated with three dimensional helmholtz type equations is investigated the resulting system of linear algebraic equations is ill conditioned and therefore its solution is regularized by employing the zeroth order tikhonov functional while the choice of the regularization parameter is based on the l curve method numerical results are presented for under equally and over determined cauchy problems in a piecewise smooth geometry the convergence accuracy and stability of the method with respect to increasing the number of source points and the distance between the source points and the boundary of the solution domain and decreasing the amount of noise added into the input data respectively are analysed

a new boundary element formulation for two and three dimensional thermoelasticity using particular integrals new two and three dimensional boundary element formulations are developed for steady state and transient uncoupled thermoelasticity these new procedures differ from previous work in that additional surface or volume integration is not required to incorporate thermal loads in the analysis instead thermal body forces are introduced in the boundary element system via particular integrals the present formulation is implemented in a general purpose multi region system and examples are presented to demonstrate the accuracy and versatility of the method

diagonals of green s functions and applications abstract we describe the diagonal of the green s function for some sturm liouville operators as it was introduced and studied in a number of papers already and we discuss a number of applications that depend on its properties semilinear elliptic pde s with rotationally invariant and possibly singular coefficients with power type nonlinearities provide a particularly well suited class of examples where the results of this article apply

the two dimensional o n nonlinear σ model renormalisation and effective actions we establish the existence of the wilson renormalised trajectory of theo n sigma model in perturbation theory in the effective charge this yields a proof of perturbative renormalisability and is also relevant in the small field analysis of the rigorous renormalisation group construction of the continuum theory

existence and nonexistence of positive radial solutions for some semilinear elliptic problems in annular domains au f x u 0 in s u 0 on xj when n is some annulus and the above conditions in 4 29 are not necessarily satisfied in fact in our main result theorem 2 4 f is not necessarily c lim f t u u may not exist or may be u rn finite and f t u could be zero for u in some finite interval 0 p we also allow lim f t u u 0 corollary 2 6 and lim f t u u may not exist in example 2 3 below u o u 0 neither lim f u u nor lim f u u exists on the other hand we show that u 0 u m

mild integrability conditions for global solutions of an elliptic equation abstract it is shown that the equation u p x u 0 has positive radially symmetric solutions on a given exterior domain e a xe r n x a 0 which behave asymptotically as x like constant multiples of the radial solutions v1 1 and v2 x n 2 of v 0 provided that p p t satisfies certain integrability conditions on a the integrability conditions are weaker than those usually imposed

radial solutions of a polyharmonic equation with power nonlinearity abstract we classify the regular radial solutions of the equation m u u u p 1 with m a positive integer and p 1 any such solution u is uniquely determined by the center values of u and its iterated laplacians up to order m 1 that is by the center point u 0 u 0 m 1 u 0 most solutions have finite exit radius that is they are unbounded and defined on open balls of finite radius are eventually monotonic with respect to the radial variable and diverge to or the center points of these solutions form two open half spaces in r m separated by an m 1 dimensional manifold m solutions with center points on m are either global or they have finite exit radius and oscillate about 0 with unbounded amplitude our results yield precise information regarding the existence multiplicity and nature of large radial solutions of m u u u p 1 on a ball of given radius

renormalization group flow of a hierarchical sine gordon model by partial differential equations we use a renormalization group differential equation to rigorously control the renormalization group flow in a hierarchical lattice sine gordon field theory in the kosterlitz thouless phase

green s function harmonic transplantation and best sobolev constant in spaces of constant curvature ass rrac t we extend the method of harmonic transplantation ft om euclidean domains to spaces of constant positive or negative curvature to this end the structure of the green s function of the corresponding laplacebeltrami operator is investigated by means of isoperimetric inequalities we derive complementary estimates for its distribution function we apply the method of harmonic transplantation to the question of whether the best sobolev constant for the critical exponent is attained i e whether there is an extremal function for the best sobolev constant in spaces of constant curvature a fairly complete answer is given based on a concentration compactness argument and a pohozaev identity the result depends on the curvature

a critical elliptic problem for polyharmonic operators abstract in this paper we study the existence of solutions for a critical elliptic problem for polyharmonic operators we prove the existence result in some general domain by minimizing on some infinite dimensional finsler manifold for some suitable perturbation of the critical nonlinearity when the dimension of domain is larger than critical one for the critical dimensions we prove also the existence of solutions in domains perforated with the small holes some unstable solutions are obtained at higher level sets by coron s topological method provided that the minimizing solution does not exist

existence of infinitely many spike solutions for a critical henon type biharmonic equation abstract following the idea of wei and yan 32 with new ingredients to take care of the critical dimension n 5 we construct infinitely many solutions of the biharmonic equation 2 v x v n 4 n 4 in the unit ball of r n n 5 0 with the navier conditions v v 0 on the boundary

radial entire solutions to even order semilinear elliptic equations in the plane semilinear elliptic equations of the form are considered where m is the m th iterate of the two dimensional laplacian p t is continuous in 0 and f u is continuous and positive either in 0 or in our main objective is to present conditions on p and f which imply the existence of radial entire solutions to that is those functions of class c 2 m 2 which depend only on x and satisfy pointwise in 2 first necessary and sufficient conditions are established for equation with p t 0 in 0 to possess infinitely many positive radial entire solutions which are asymptotic to positive constant multiples of x 2 m 2 log x as x secondly it is shown that in the case p t f u 0 is nondecreasing in equation always has eventually negative radial entire solutions all of which decrease at least as fast as negative constant multiples of x 2 m 2 log x as x our results seem to be new even when specialised to the prototypes where is a constant

entire solutions of a class of even order quasilinear elliptic equations on demontre l existence de solutions entieres radialement symetriques et on decrit leur comportement asymptotique pour x

regularized mfs solution of inverse boundary value problems in three dimensional steady state linear thermoelasticity abstract we investigate the numerical reconstruction of the missing thermal and mechanical boundary conditions on an inaccessible part of the boundary in the case of three dimensional linear isotropic thermoelastic materials from the knowledge of over prescribed noisy data on the remaining accessible boundary we employ the method of fundamental solutions mfs and several singular value decomposition svd based regularization methods e g the tikhonov regularization method tikhonov and arsenin 1986 the damped svd and the truncated svd hansen 1998 whilst the regularization parameter is selected according to the discrepancy principle morozov 1966 generalized cross validation criterion golub et al 1979 and hansen s l curve method hansen and o leary 1993

critical dimension of a hessian equation involving critical exponent and a related asymptotic result abstract let s k 2 u 1 k n 2 be the k th hessian operator we study the problem formula where k is the critical exponent for s k and is a ball results generalizing those obtained by brezis nirenberg for the special case k 1 are established a discussion 8 on the asymptotic behavior of solutions of the problem as 0 is also included

numerical solution of the cauchy problem for steady state heat transfer in two dimensional functionally graded materials the application of the method of fundamental solutions to the cauchy problem for steady state heat conduction in two dimensional functionally graded materials fgms is investigated the resulting system of linear algebraic equations is ill conditioned and therefore regularization is required in order to solve this system of equations in a stable manner this is achieved by employing the zeroth order tikhonov functional while the choice of the regularization parameter is based on the l curve method numerical results are presented for both smooth and piecewise smooth geometries the convergence and the stability of the method with respect to increasing the number of source points and the distance between the source points and the boundary of the solution domain and decreasing the amount of noise added into the input data respectively are analysed