nodal type bound states of schrodinger equations via invariant set and minimax methods for nonlinear schrodinger equations in the entire space we present new results on invariant sets of the gradient flows of the corresponding variational functionals the structure of the invariant sets will be built into minimax procedures to construct nodal type bound state solutions of nonlinear schrodinger type equations 2004 elsevier inc all rights reserved

multiple solutions of nonlinear schrodinger equations via flow invariance and morse theory we prove the existence of multiple bound states of the nonlinear schrodinger equation u v x u f u here the linear potential v is continuous and bounded from below and the nonlinearity f is of asymptotically linear type we show that under certain assumptions on the spectrum of the schrodinger operator v and the asymptotic behaviour of f u u the above equation has at least four non trivial solutions two of them sign changing

invariant sets of descending flow in critical point theory with applications to nonlinear differential equations abstract properties of invariant sets of descending flow defined by a pseudogradient vector field of a functional in a banach space are studied in this way several critical points can be found by constructing different invariant sets on which the functional is bounded below under suitable conditions the existence of at least four critical points of a functional is proved each critical point being in a certain invariant set the theoretical results are applied to nonlinear elliptic boundary value problems and nonlinear systems of ordinary differential equations in variant cases at least four solutions are obtained for these equations

coexistence diameter in two dimensional colloid polymer mixtures we demonstrate that the law of the rectilinear coexistence diameter in two dimensional mixtures of nonspherical colloids and nonadsorbing polymers is violated upon approach to the critical point the diameter shows logarithmic singular behavior governed by a term t ln t with t the relative distance from the critical point no sign of a term t2beta could be detected with beta the critical exponent of the order parameter indicating a very weak or absent yang yang anomaly our analysis thus reveals that nonspherical particle shape alone is not sufficient for the formation of a pronounced yang yang anomaly in the critical behavior of fluids

homoclinic orbits for a class of first order nonperiodic asymptotically quadratic hamiltonian systems with spectrum point zero in this paper we study the existence and multiplicity of homoclinic orbits for a class of first order nonperiodic hamiltonian systems by applying two recent critical point theorems for strongly indefinite functionals we give some new criteria to guarantee that hamiltonian systems with asymptotically quadratic terms and spectrum point zero have at least one and a finite number of pairs of homoclinic orbits under some adequate conditions respectively

on hamiltonian elliptic systems with periodic or non periodic potentials abstract this paper is concerned with the following hamiltonian elliptic system u b x u v x u h v x u v v b x v v x v h u x u v for x r n existence and multiplicity of solutions are obtained for the systems with periodic or non periodic potentials v via variational methods

multiple solutions for a semiclassical schrodinger equation abstract this paper is concerned with the semiclassical nonlinear schrodinger equation e 2 u v x u f x u x r n u x 0 as x where e 0 is a small parameter under certain hypotheses on v and a general spectral assumption the existence and multiplicity of semiclassical solutions are obtained for asymptotically linear nonlinearity via variational methods

on ground state solutions for some non autonomous schrodinger poisson systems abstract in this paper we study the schrodinger poisson system sp u u k x x u a x f u in r 3 k x u 2 in r 3 and prove the existence of ground state solutions for system sp under certain assumptions on the linear and nonlinear terms some recent results from different authors are extended

solutions of a schrodinger poisson system with combined nonlinearities abstract in this paper we are concerned with the following schrodinger poisson system u v x u u k x u q 2 u f x u x r 3 u 2 lim x x 0 x r 3 where 0 is a parameter 1 q 2 and f x u is linearly bounded in u at infinity we establish the existence and multiplicity of solutions under suitable assumptions on v k and f

unique continuation and absence of positive eigenvalues for schrodinger operators on considere l operateur de laplace sur r n et une fonction v x sur un sous ensemble connexe ouvert de r n on montre que si n 3 une propriete de prolongement unique est vraie pour v l loc n 2 r n dans l espace de sobolev h loc 2 q r n avec q 2n n 2

morse index and multiple solutions for the asymptotically linear schrodinger type equation abstract we study the nonlinear problem u v x u f x u x r n where the schrodinger type operator v is semibounded and has a finite number of eigenvalues below the infimum of the essential spectrum we classify the linear schrodinger equation prove the semi continuity and monotonicity of the index function and obtain some new conditions on the existence and multiplicity for generalized asymptotically linear schrodinger equations based on an application of the classical ambrosetti rabinowitz symmetric mountain pass theorem

on a class of asymptotically linear elliptic problems in rn under these conditions p is an asymptotically linear problem when this equation is considered in a bounded domain 0 r with say the dirichlet boundary condition there is a large literature on existence and multiplicity results of particular interest is then the case of resonance where s and s is the asymptotic linearization of the problem in other words s d s l 0 l 0 is the operator given by

on the asymptotic distribution of the eigenvalue branches of the schrodinger operator h λw in a spectral gap of h on considere des operateurs de schrodinger h v dans l espace de hilbert l 2 r avec un potentiel v satisfaisant 1 vel r on suppose que l intervalle a b est contenu dans l ensemble resolvant de h on obtient des estimations asymptotiques sur le nombre des branches de valeurs propes dans a b des familles d operateurs h w 0 quand ou w est un potentiel a courte portee non negatif

the fucik spectrum of schrodinger operator and the existence of four solutions of schrodinger equations with jumping nonlinearities abstract this paper contains the existence of four solutions of schrodinger equations with jumping nonlinearities the proof procedure is supported by a lot of new results initially a consequence is rendered as a minimax principle on h 1 r n which allows us to achieve the feasibility verification of the ps condition furthermore the constructions of minimal and maximal curves of fucik spectrum in q l see the introduction for the definition of q l warrant an intensive investigation that we encounter some thorny problems is largely due to the absence of compact embedding and the appearance of essential spectrum based on a nontrivial argument we can compute critical groups of homogeneous functional at zero if a b is free of fucik spectrum and a b q l this together with convexity and concavity offers a detailed description of the two curves by a series of sophisticated tricks additionally we present a new version of morse theory in view of the fact that classical version doesn t work directly for weak smooth functional on h 1 r n finally we prove a weak maximum principle for r n which serves as a tool to get a critical point in positive and negative cone respectively and also compute critical groups of critical points of mountain pass type with the help of above preparations we attain the ultimate aim by morse inequalities and various exact homology sequences

the existence of a positive solution to asymptotically linear scalar field equations which is important in using the mountain pass theorem the aim of this paper is to discuss how to use the mountain pass theorem to show the existence of a positive solution to the present problem when we lose the above condition furthermore if f x u f u we also prove that the above problem has a ground state by using the articial constraint method

existence and multiplicity of solutions for asymptotically linear nonperiodic hamiltonian elliptic system abstract this paper is concerned with the following nonperiodic hamiltonian elliptic system u v x u h v x u v v v x v h u x u v x r n u x v x 0 as x where z u v r n r r n 3 assuming the potential v is nonperiodic and sign changing h x z is nonperiodic in x and asymptotically quadratic in z u v existence and multiplicity of solutions are obtained via a variational approach

sign changing solutions of a class of nonlocal quasilinear elliptic boundary value problems abstract this paper is concerned with nonlocal kirchhoff s equation a b u 2 u f x u in u 0 on via variational methods and invariant sets of descent flow we obtain existence of signed and sign changing solutions with asymptotically 3 linear bounded nonlinearity

multiple solutions for a schrodinger type equation with an asymptotically linear term abstract we study the nonlinear schrodinger type equation u g x 1 u f u on the whole space r n the nonlinearity f is assumed to be asymptotically linear and g x 0 has a potential well using results from critical point theory we show how the behavior of f near zero and at infinity affects the number of solutions

on the existence of eigenvalues of the schrodinger operatorh λw in a gap of σ h the authors prove a number of results asserting the existence of eigenvalues of the schrodinger operatorh w in a gap of h whereh v andv andw are bounded the existence of these eigenvalues is an important element in the theory of the colour of crystals the basic theorems are proved in v stronger results forv 1 are also presented

compactness results for schrodinger equations with asymptotically linear terms abstract we study the nonlinear problem u v x f x u x r n lim x u x 0 where the schrodinger operator v is semibounded and the nonlinearity f is linearly bounded we establish compactness of palais smale sequences and cerami sequences for the associated energy functional under general spectral theoretic assumptions applying these results we obtain existence of three nontrivial solutions if the energy functional has a mountain pass geometry

near field computation for sound propagation above ground using complex image theory in this paper a very simple method is introduced for the efficient computation of the sound field in the near region above an impedance ground or an extended reaction ground the procedure is based on complex image theory using prony s method the slowly varying factor in the integrand of the sommerfeld integral is approximated by a short series in terms of complex exponential functions the result can be exactly evaluated by the sommerfeld identity a new closed form approximate expression of the sound field is obtained which is represented as the original source its quasistatic image and several images with complex amplitudes and positions avoiding numerical evaluation of the sommerfeld integral makes these closed form expressions computationally very efficient the representation of the field with complex images makes the formula useful in measurement of ground impedance or in other cases requiring repeated mapping of the sound field numerical results show that these closed form green s functions are very accurate for the computation of the near field