ground state sign changing solutions for asymptotically cubic or super cubic schrodinger poisson systems without compact condition abstract this paper is dedicated to studying the following schrodinger poisson system u v x u u k x f u x r 3 u 2 x r 3 where v k c r 3 r and f c r r under mild assumptions on the decay rate of v x we establish the existence of one ground state sign changing solution with precisely two nodal domains by using a weaker growth condition lim t 0 t f s d s t 3 instead of the usual super cubic condition lim t 0 t f s d s t 4 our result unifies both asymptotically cubic and super cubic cases which generalizes and improves the corresponding ones in the literatures

mouvement brownien cones et processus stables letw wt t 0 denote a two dimensional brownian motion starting at 0 and for 0 4 here we construct a measure a local time supported onh for 4 2 the brownian motionw time changed by the inverse of this local time is shown to be a two dimensional stable process with index 2 2 this results extends spitzer s construction of the cauchy process which is recovered by taking 2 a formula which describes the behaviour ofw before a timet h is established and applied to the proof of a conjecture of burdzy we also obtain a two dimensional version of the famous theorem of levy concerning the maximum process of linear brownian motion precisely for 0 2 letst denote the vertex of the smallest wedge of the typez c which contains the path ofw up to timet the processst wt is shown to be a reflected brownian motion in the wedgec with oblique reflection on the sides finally we investigate various extensions of the previous results to brownian motion inrd d 3 letc be the cone associated with an open subset of the spheresd 1 and leth be defined ash above sufficient conditions are given forh to contain nonzero times in terms of the first eigenvalue of the dirichlet laplacian on

a class of path valued markov processes and its applications to superprocesses let s be a continuous markov process satisfying certain regularity assumptions we introduce a path valued strong markov process associated with s which is closely related to the so called superprocess with spatial motion s in particular a subseth of the state space of s intersects the range of the superprocess if and only if the set of paths that hith is not polar for the path valued process the latter property can be investigated using the tools of the potential theory of symmetric markov processes a set is not polar if and only if it supports a measure of finite energy the same approach can be applied to study sets that are polar for the graph of the superprocess in the special case when s is a diffusion process we recover certain results recently obtained by dynkin

cone paths for the planar brownian snake for the brownian path valued process of le gall or brownian snake in bbb r 2 the times at which the process is a cone path are considered as a function of the size of the cone and the terminal position of the path the results show that the paths for the path valued process have local properties unlike those of a standard brownian motion

ground state sign changing solutions for a schrodinger poisson system with a 3 linear growth nonlinearity abstract in this paper we investigate the existence and asymptotic behavior of ground state sign changing solutions to a class of schrodinger poisson systems u v x u u f x u u 2 u x r 3 u 2 x r 3 where v is a smooth function f is nonnegative 0 1 and 1 is the first eigenvalue of the problem u v x u f x u in h with the help of the sign changing nehari manifold we obtain that the schrodinger poisson system possesses at least one ground state sign changing solution u for all 0 and each 1 moreover we prove that its energy is strictly larger than twice that of ground state solutions besides we give a convergence property of u as 0 this paper can be regarded as the complementary work of shuai and wang 23 wang and zhou 24

schrodinger poisson equations without ambrosetti rabinowitz condition abstract we prove the existence of ground state solutions for a stationary schrodinger poisson equation in r 3 the proof is based on the mountain pass theorem and it does not require the ambrosetti rabinowitz condition

nondifferentiable multiplier rules for optimization and bilevel optimization problems in this paper we study optimization problems with equality and inequality constraints on a banach space where the objective function and the binding constraints are either differentiable at the optimal solution or lipschitz near the optimal solution necessary and sufficient optimality conditions and constraint qualifications in terms of the michel penot subdifferential are given and the results are applied to bilevel optimization problems

positive 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 u p 1 u x r 3 k x u 2 x r 3 with p 3 5 assuming that a r 3 r and k r 3 r are nonnegative functions such that lim x a x a 0 lim x k x 0 and satisfying suitable assumptions but not requiring any symmetry property on them we prove the existence of positive solutions

boundedness of certain sets of lagrange multipliers in vector optimization in this paper we establish lagrange multiplier rules in terms of michel penot subdifferential for nonsmooth vector optimization problem a constraint qualification or regularity condition in terms of michel penot subdifferential is given and under this regularity condition the boundedness of certain sets of lagrange multipliers are discussed

ground state and bounded state solution for the nonlinear fractional choquard schrodinger poisson system in this paper we study a class of fractional choquard schrodinger poisson system under some suitable assumptions by using a variational approach we establish the existence of non negative ground state solution and also discuss the nonexistence of ground states moreover we prove the existence of bounded state by using a linking theorem

points cones du mouvement brownien plan le cas critique letb bt t 0 be a planar brownian motion and let 0 for anyt 0 the pointz bt is called a one sided cone point with angle if there exist e 0 and a wedgew z with vertexz and angle such thatbs w z for everys t t e burdzy and shimura have shown independently that one sided cone points with angle exist when 2 but not when 2 the present paper deals with the critical case 2 we show that cone points with angle 2 do not exist

stationary solutions of non autonomous maxwell dirac systems abstract the maxwell dirac system describes the interaction of a particle with its self generated electromagnetic field in this paper we study the existence of least energy stationary solutions for non autonomous maxwell dirac system with a nonlinear term in 3 1 minkowski space time via variational methods this problem is strongly indefinite and presents a lack of compactness to overcome these difficulties we will use the linking and concentration compactness arguments

existence of ground state solutions of nehari pohozaev type for fractional schrodinger poisson systems with a general potential abstract in this paper we consider the following fractional schrodinger poissonproblem s u v x u u f u in r 3 t u 2 in r 3 where 0 s t 1 and 2 s 2 t 3 the potential v x is weakly differentiable and f c r r by introducing some new tricks we prove that the problem admits a ground state solution of nehari pohozaev type under mild assumptions on v and f the results here extend the existing study

positive solutions for a schrodinger poisson system with singularity and critical exponent abstract we study multiplicity of positive solutions for a class of schrodinger poisson system with singularity and critical exponent and obtain two positive solutions via the variational and perturbation 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

infinitely many positive solutions for a schrodinger poisson system abstract we are interested in the existence of infinitely many positive solutions of the schrodinger poisson system u u v x u u p 1 u x r 3 v x u 2 x r 3 where v x is a positive bounded function 1 p 5 and v r r x has the following decay property v r a r m o 1 r m with a 0 m 3 2 0 the solutions obtained are non radial

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

multiple solutions for a nonlinear schrodinger poisson system with sign changing potential this paper deals with the existence and multiplicity of nontrivial solutions for a nonlinear schrodinger poisson system under some suitable conditions some criteria on the existence of nontrivial solutions including a ground state solution two solutions and a sequence of nontrivial solutions u k with u k 0 as k is established by applying the morse theory and variational methods some known results in the literatures are extended and improved

on ground state solutions for the schrodinger poisson equations with critical growth abstract in this paper we study the existence of ground state solutions for the following schrodinger poisson equation u v x u u u q 1 u u 4 u in r 3 u 2 in r 3 where is a positive parameter under some certain assumptions on v we prove that for every 0 and q 2 5 such a class of schrodinger poisson equation with critical growth has at least a positive ground state solution via variational methods some recent results from the literature are extended

regularizing effect for some p laplacian systems abstract we study existence and regularity of weak solutions for the following p laplacian system p u a 1 u r 2 u f u w 0 1 p p u r w 0 1 p where is an open bounded subset of r n n 2 p v div v p 2 v is the p laplacian operator for 1 p n a 0 r 1 0 p 1 and f belongs to a suitable lebesgue space in particular we show how the coupling between the equations in the system gives rise to a regularizing effect producing the existence of finite energy solutions

the existence and concentration of positive solutions for a nonlinear schrodinger poisson system with critical growth we consider the schrodinger poisson system e2 u v x u x u f u u2 in r3 where the nonlinear term f is of critical growth in this paper we construct a solution u of the above elliptic system which concentrates at an isolated component of positive locally minimum points of v as 0 under certain conditions on f in particular the monotonicity of f s s3 and the so called ambrosetti rabinowitz condition are not required

a lagrange multiplier rule with small convex valued subdifferentials for nonsmooth problems of mathematical programming involving equality and nonfunctional constraints it is shown that a lagrange multiplier rule involving the michel penot subdifferentials is valid for the problem minimizef0 x subject tofi x 0 i 1 m fi x 0 i m 1 n x q where all functionsf are lipschitz continuous andq is a closed convex set the proof is based on the theory of fans

necessary conditions in nonsmooth optimization the paper contains four theorems concerning first order necessary conditions for a minimum in nonsmooth optimization problems in banach spaces a lagrange multiplier rule for a mathematical programming problem in which an infinite dimensional equality constraint is included in the constraints a general maximum principle for nonsmooth optimal control problems with state constraints and a kind of multiplier rule for mathematical programming problems which applies when only finitely many equality constraints are present but when the lipschitz continuity assumptions are removed a summary of relevant background results from analysis is provided

the thomas fermi von weizsacker theory of atoms and molecules we place the thomas fermi von weizsacker model of atoms on a firm mathematical footing we prove existence and uniqueness of solutions of the thomas fermi von weizsacker equation as well as the fact that they minimize the thomas fermi von weizsacker energy functional moreover we prove the existence of binding for two very dissimilar atoms in the frame of this model

on the potential theory of symmetric markov processes on reprend des resultats de dynkin et on considere un processus de markov fort symetrique continu a droite on etudie la relation existant entre le cone de mesures positives d energie finie et la capacite

multiplicity of small negative energy solutions for a class of nonlinear schrodinger poisson systems this paper deals with the following nonlinear schrodinger poisson email protected v x u k x f x u h x f x u inr 3 email protected f k x u 2 inr 3 where v x k x and h x are nonnegative continuous functions under appropriate assumptions on v x k x h x and f x u we prove the existence of infinitely many small negative energy solutions by using the variant fountain theorem established by zou recent results from the literature are extended

existence and nonexistence of positive solutions for a static schrodinger poisson slater equation abstract in this paper we study the following type of the schrodinger poisson slater equation with critical growth u u 2 1 4 x u u p 1 u u 4 u in r 3 where 0 and p 11 7 5 for the case of p 2 5 we develop a novel perturbation approach together with the well known mountion pass theorem to prove the existence of positive ground states for the case of p 2 we obtain the nonexistence of nontrivial solutions by restricting the range of and also study the existence of positive solutions by the constrained minimization method for the case of p 11 7 2 we use a truncation technique developed by brezis and oswald 9 together with a measure representation concentration compactness principle due to lions 27 to prove the existence of radial symmetrical positive solutions for 0 with some 0 the above results nontrivially extend some theorems on the subcritical case obtained by ianni and ruiz 18 to the critical case

semiregularity and generalized subdifferentials with applications to optimization the michel penot subdifferential of a locally lipschitzian function is the principal part of the clarke subdifferential it coincides with the g derivative at differentiable points a locally lipschitzian function can be determined by its michel penot subdifferential uniquely up to an additive constant though this cannot be done by its clarke subdifferential if the set of abnormal points is not negligible a set valued operator is the michel penot subdifferential of a locally lipschitzian function if and only if it is a seminormal operator satisfying a cyclical condition various calculus rules hold for the michel penot subdifferential equalities hold for these rules at a point under semiregularity which is weaker than regularity for a locally lipschitzian function in a separable banach space semiregularity holds everywhere except for a haar zero set applications in optimization are discussed

multiple positive solutions for a schrodinger newton system with sign changing potential abstract in this paper we study the schrodinger newton systems with sign changing potential in a bounded domain by using the variational method and analytic techniques the existence and multiplicity of positive solutions are established

an asymptotically linear schrodinger poisson system on r3 abstract in this paper we are concerned with the following nonlinear schrodinger poisson equation u u u f x u u x r 3 u 2 lim x x 0 where u r 3 r are positive functions the parameters 0 f x s tend to p x and q x l r 3 respectively as s 0 and s under some simple assumptions on f x s we give existence and nonexistence results depending on the parameters and

existence and multiplicity of stationary solutions for a class of maxwell dirac system abstract this paper is concerned with the following maxwell dirac system i k 1 3 k k u a u m x u k x u f u x u 4 k x u 2 in r 3 where m x is a external potential and f x u is an asymptotically quadratic nonlinearity modeling various types of interactions in view of the effects of the nonlocal term we use some special techniques to deal with the nonlocal term moreover existence and multiplicity of stationary solutions are obtained for system without any periodicity assumption via variational methods

multi bump solutions for the nonlinear schrodinger poisson system in this paper we study a kind of nonlinear schrodinger poisson system with a parameter e for any positive integer m we prove that there exists e m 0 such that for 0 e e m the equation has an m bump positive solution under some suitable conditions as a consequence the equation has more and more multi bump positive solutions as e 0

multiple solutions for a class of schrodinger poisson system with indefinite nonlinearity in this article we investigate the existence and multiplicity of solutions of schrodinger poisson system u u l x u k x u 2u h x u x r3 l x u2 x r3 where the potential k x allows sign changing we obtain the existence and multiplicity of solutions for the system which can be regarded as complementary work of huang et al 2013 12