an orlicz space approach to superlinear elliptic systems in this paper we study superlinear elliptic systems in hamiltonian form using an orlicz space setting we extend the notion of critical growth to superlinear nonlinearities which do not have a polynomial growth existence of nontrivial solutions is proved for superlinear nonlinearities which are subcritical in this generalized sense

existence and multiplicity of solutions for an elliptic system with nonlinear boundary conditions abstract in this paper we prove the existence and multiplicity of solutions for the elliptic system u u v v in with nonlinear coupling at the smooth boundary given by u h u v h v on where is a bounded domain of r n with smooth boundary is the outer normal derivative the proofs are done under suitable assumptions on the hamiltonian and based on the local linking theorem and a multiple critical points theorem of the critical point theory

liouville theorem for elliptic equations with nonlinear boundary value conditions and finite morse indices abstract in this paper we study the nonexistence result for the following nonlinear elliptic equation with nonlinear boundary value condition u u p 1 u in r n u u q 1 u on r n if 1 p n 2 n 2 1 q n n 2 and p q n 2 n 2 n n 2 then we will show that this problem does not possess nontrivial bounded solution with finite morse index

a superquadratic indefinite elliptic system and its morse conley floer homology we study critical points of the indefinite functional f h u v int nabla u cdot nabla v h x u v mathrm d x by applying floer s homology construction to the ordinary gradient flow of the functional f on a suitable sobolev space one of our main observations is that even though this flow is well posed in both time directions and lacks any kind of smoothing property one can still obtain compactness of connecting orbit spaces and thus define the floer homology for f h

an infinite dimensional morse theory with applications in this paper we construct an infinite dimensional extraordinary cohomology theory and a morse theory corresponding to it these theories have some special properties which make them useful in the study of critical points of strongly indefinite functionals by strongly indefinite we mean a functional unbounded from below and from above on any subspace of finite codimension several applications are given to hamiltonian systems the onedimensional wave equation of vibrating string type and systems of elliptic partial differential equations 0 introduction let e be a real hilbert space with an inner product and let be a twice continuously differentiable functional denote the frechet derivative and the gradient of at x by x and x respectively where as usual x y x y y e recall that a point x0 e is said to be critical if x0 0 or equivalently if x0 0 the level c r will be called regular if 1 c contains no critical points and critical if x0 0 for some x0 1 c let a b a b be two regular levels of denote m 1 a b and consider the restriction of to m in morse theory one is interested in the local topological structure of the level sets of m near a critical point and in the relation between this local structure and the topological structure of the set m to be more specific suppose that x0 m is an isolated critical point of then one defines a sequence of critical groups of at x0 by setting cq x0 hq c u u x0 q 0 1 2 0 1 where c x0 c x e x c hq is the q th singular homology group with coefficients in some field f and u is a neighbourhood of x0 define the morse index of x0 to be the maximal dimension of a subspace of e on which the quadratic form x0 y y is negative definite one shows that if x0 is a nondegenerate critical point i e if x0 e e is invertible then cq x0 f received by the editors march 20 1995 1991 mathematics subject classification primary 58e05 secondary 34c25 35j65 35l05 55n20 58f05

ground states for diffusion system with periodic and asymptotically periodic nonlinearity in this paper we study the following diffusion system t u x u b t x x u v x u g t x v t v x v b t x x v v x v f t x u where b c 1 r r n r n and v x c r n r by using non nehari manifold method developed in tang 2014 we investigate the existence of the ground state solutions of nehari type for the above problem with periodic and asymptotically periodic nonlinearity

infinitely many solutions for symmetric and non symmetric elliptic systems we study an elliptic system equivalent to a fourth order elliptic equation by using variational and perturbative methods we prove the existence of infinitely many solutions both in the symmetric and in the non symmetric case

multiple solutions for asymptotically linear elliptic systems in this article we consider cooperative and noncooperative elliptic systems that are asymptotically linear at infinity we obtain infinitely many solutions with small energy if the potential is even if the noncooperative system is resonant both at zero and at infinity then the number of nontrivial solutions depends on the dimension of the eigenspaces between resonant values

on a nonlinear elliptic system with symmetric coupling abstract multiplicity results are proved for the nonlinear elliptic system u g v 0 v g u 0 in u v 0 on where r n is a bounded domain with smooth boundary and g r r is a nonlinear c 1 function which satisfies additional conditions no assumption of symmetry on g is imposed extensive use is made of a global version of the lyapunov schmidt reduction method due to castro and lazer and of symmetric versions of the mountain pass theorem

infinitely many solutions for non cooperative elliptic systems in this paper we consider the existence of infinitely many solutions of noncooperative elliptic systems perturbed from odd cases

existence and multiplicity of solutions for asymptotically hamiltonian elliptic systems in rn abstract this paper is concerned with the following nonperiodic hamiltonian elliptic system u v x u h u x u v in r n v v x v h v x u v in r n u x 0 and v x 0 as x where the potential v is bounded below and h is asymptotically linear in z as z with z u v by applying a generalized linking theorem of strongly indefinite functionals we obtain solutions for the above system

ground state solutions for superquadratic hamiltonian elliptic systems with gradient terms abstract in this paper we study the following hamiltonian elliptic system with gradient terms 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 where v x b x and h x u v are 1 periodic in x under weak superquadratic assumptions for the nonlinearities we use much more direct methods to prove that all the cerami sequences for the energy functional are bounded and establish the existence of ground state solutions for this system

on a singular elliptic system with quadratic growth in the gradient abstract in this paper we deal with the following singular elliptic system u u 2 u p p q a x v q u p 2 u f x r n v v 2 v q p q a x u p v q 2 v g x r n where n 3 n 2 4 p q 1 and p q n 2 n 2 we show through the sub and supersolutions method the existence of a nonnegative solution for an approximated system the limit of the approximated solution is a positive solution in the case 0 p q and f g we prove the uniqueness of a solution among others we prove some existence and uniqueness results for some auxiliary problems by using the comparison principle a minimization method and with the help of nehari manifold the proofs rely on the concentration compactness principle

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

a note on superlinear hamiltonian elliptic systems this paper is concerned with the superlinear periodic elliptic systems of hamiltonian type in the whole space the existence of a ground state solution as well as an infinite number of geometrically distinct solutions is obtained

existence and multiplicity of solutions for asymptotically linear noncooperative elliptic systems abstract using the minimax methods in critical point theory and a generalized landesman lazer type condition we establish two existence results of solutions for asymptotically linear noncooperative elliptic systems at resonance besides this we obtain two solutions in the case of near resonance

infinitely many solutions for diffusion equations without symmetry abstract we consider the following diffusion system t u x u b t x x u v x u h v t x u v t v x v b t x x v v x v h u t x u v t x r r n which is an unbounded hamiltonian system in l 2 r r n r 2 m z u v r r n r m r m b c r r n r n v c r n r and h c 1 r r n r 2 m r suppose that h b and v depend periodically on t and x and that h t x z is superquadratic in z as z without a symmetry assumption on h we establish the existence of infinitely many geometrically distinct solutions via a variational approach

on conservation and dual consistency for summation by parts based approximations of parabolic problems we consider the coupling of parabolic problems discretized using difference operators on summation by parts sbp form with interface conditions imposed weakly in 1 2 it was shown that conserv

new linking theorem and elliptic systems with nonlinear boundary condition in this paper we establish a new linking theorem without ps type assumption the new theorem produces bounded ps sequences the abstract result will be used to study the existence of nontrivial positive solutions to the elliptic system u u v v in with nonlinear boundary condition u gv u gu on where is a bounded domain of rn with smooth boundary is the outer normal derivative we consider weak superlinear and asymptotically linear cases

on the existence of positive solutions of a perturbed hamiltonian system in rn using the legendre fenchel transformation and the mountain pass theorem due to ambrosetti and rabinowitz we establish an existence result for perturbations of periodic and asymptotically periodic semilinear hamiltonian systems of the type pw u u w2 x v p 1vinrn v v w1 x u q 1uinrn u x v x 0as x u 0 v 0inrn n 2 here the numbers p q 1 are below the critical hyperbola if n 3 that is they satisfy 1 p 1 1 q 1 n 2 n while no additional restrictions on p and q are required if n 2 the functions wi i 1 2 are bounded positive continuous functions

the nehari manifold for systems of nonlinear elliptic equations abstract this paper deals with the existence and multiplicity results of nonlocal positive solutions to the following system p u u p 1 2 u 1 u u 1 v 1 q v v q 2 v 1 u 1 v 1 v together with dirichlet or mixed boundary conditions under some hypotheses on the parameters p p 1 and q more precisely the system considered corresponds to a perturbed eigenvalue equation combined with a second equation having concave and convex nonlinearities the study is based on the extraction of palais smale sequences in the nehari manifold the behaviour of the energy corresponding to these positive solutions with respect to the real parameters and is established

multiple positive solutions of strongly indefinite systems with critical sobolev exponents and data that change sign abstract in this paper we study the existence of multiple positive solutions to some hamiltonian elliptic systems v u u p 1 u ef x u v v q 1 v eg x in u 0 v 0 in u v 0 on where is a smooth bounded domain in r n n 3 f g c 1 p q 1 r for the subcritical and critical cases we prove that problem has at least two positive solutions for any e 0 e and has no positive solutions for any e e e in the supercritical case we find that the existence of solutions of problem for 0 is closely related to the existence of nonnegative solutions of some linear elliptic system

nonnegative solutions for nonlinear elliptic systems abstract in this paper we show that the semilinear elliptic systems of the form 0 1 u v g v v u f u x u v 0 x possess at least one nonnegative nontrivial solution pair u v h 0 1 h 0 1 where is a smooth bounded domain in r n

soliton solutions to systems of coupled schrodinger equations of hamiltonian type we study the existence of positive solutions of hamiltonian type systems of second order elliptic pde in the whole space the systems depend on a small parameter and involve a potential having a global well structure we use dual variational methods a mountain pass type approach and fourier analysis to prove positive solutions exist for sufficiently small values of the parameter

on a new class of elliptic systems with nonlinearities of arbitrary growth abstract we guarantee the existence of infinitely many different pairs of solutions to the system u v p in v f u in u v 0 on where 0 p 2 n 2 is a bounded domain in r n and the continuous nonlinear term f has an unusual oscillatory behavior the sequence of solutions tends to zero resp infinity with respect to certain norms and the nonlinear term f may enjoy an arbitrary growth at infinity resp at zero whenever f oscillates near zero resp at infinity our results provide the first applications of ricceri s variational principle in the theory of coupled elliptic systems

multiplicity result for a class of elliptic problems with non differentiable terms in rn abstract using non smooth critical point theory and a multiplicity result based on local linking the original smooth version is due to brezis and nirenberg we prove the existence of multiple solutions for a class of schrodinger type systems with non differentiable terms in r n in addition we give two examples to illustrate our multiplicity result

superconvergent functional output for time dependent problems using finite differences on summation by parts form finite difference operators satisfying the summation by parts sbp rules can be used to obtain high order accurate energy stable schemes for time dependent partial differential equations when the boundary conditions are imposed weakly by the simultaneous approximation term sat in general an sbp sat discretization is accurate of order p 1 with an internal accuracy of 2p and a boundary accuracy of p despite this it is shown in this paper that any linear functional computed from the time dependent solution will be accurate of order 2p when the boundary terms are imposed in a stable and dual consistent way the method does not involve the solution of the dual equations and superconvergent functionals are obtained at no extra computational cost four representative model problems are analyzed in terms of convergence and errors and it is shown in a systematic way how to derive schemes which gives superconvergent functional outputs

the nehari manifold for a semilinear elliptic system involving sign changing weight functions abstract in this paper we study the combined effect of concave and convex nonlinearities on the number of solutions for a semilinear elliptic system e with sign changing weight function with the help of the nehari manifold we prove that the system has at least two nontrivial nonnegative solutions when the pair of the parameters belongs to a certain subset of r 2

asymptotic behavior of solutions for henon systems with nearly critical exponent abstract we consider in this paper the problem 0 1 u x v p v x u q e x u 0 v 0 x u v 0 x where is the unit ball in r n centered at the origin 0 p n 0 n 8 p 1 q e 1 suppose q e q 1 as e 0 and q e q satisfy respectively n p 1 n q e 1 n 2 n p 1 n q 1 n 2 we investigate the asymptotic behavior of the ground state solutions u e v e of 0 1 as e 0 we show that the ground state solutions concentrate at a point which is located at the boundary in addition the ground state solution is non radial provided that e 0 is small

existence of solutions to higher order lane emden type systems abstract we prove existence results for the lane emdentype system u v q v u p in b 1 r n r u r 0 r 0 1 on b 1 r v r 0 r 0 1 on b 1 where b 1 is the unitary ball in r n n max 2 2 is the outward pointing normal n 1 and 1 is the polyharmonic operator a continuation method together with a priori estimates will be exploited moreover we prove uniqueness for the particular case 2 1 and p q 1

multiple solutions for elliptic systems with nonlinearities of arbitrary growth abstract we prove the existence of infinitely many solutions for symmetric elliptic systems with nonlinearities of arbitrary growth moreover if the symmetry of the problem is broken by a small enough perturbation term we find at least three solutions the proofs utilise a variational setting given by de figueiredo and ruf in order to prove an existence s result and the algebraic approach based on the pohozaev s fibering method

asymptotically linear schrodinger equations with sign changing potential abstract in this paper we show that the following system 0 1 u v x u g x v v v x v f x u x r n possesses at least one non trivial solution pair u v where f x t g x t are continuous functions on r n r and asymptotically linear as t and v x is allowed to be sign changing

on superquadratic elliptic systems in this article we study the existence of solutions for the elliptic system updelta u frac partial h partial v left u v x right text in upomega updelta v frac partial h partial v left u v x right text in upomega u 0 v 0 text on partial upomega where upomega is a bounded open subset of mathbb r n with smooth boundary partial upomega and the function h mathbb r 2 times overline upomega to mathbb r is of class c 1

multiplicity and concentration of solutions for elliptic systems with vanishing potentials abstract in this article we use variational methods to study a strongly coupled elliptic system depending on a positive parameter we suppose that the potentials are nonnegative and the intersection of the sets where they vanish has positive measure a technical condition imposed on the product of the potentials allows us to consider a setting where we do not assume any positive lower bound for the potentials considering the associated functional defined on an appropriated subspace of d 1 2 r n d 1 2 r n we are able to establish results on the existence and multiplicity of solutions for the system when the parameter is sufficiently large we also study the asymptotic behavior of these solutions when

existence and uniqueness of positive solution for non variational elliptic systems abstract we prove the existence of solutions for strongly coupled elliptic systems in non variational form involving second order uniformly elliptic linear operators in we also derive classes of systems having a multiplicity of solutions and the uniqueness of a solution for this purpose we use the galerkin scheme in the product of hilbert spaces using the comparison principle for systems of lane emden we compare the obtained solutions

bifurcation for an elliptic system coupled in the linear part we study linearly coupled elliptic systems without any assumption on the signs of the coefficients of the linear part we derive first the leray schauder degree of the associated linear system then we obtain sufficient conditions on the nonlinear terms for having bifurcation to coexistence states our results include the sublinear case keys words linearly coupled elliptic systems bifurcation to positive solutions coexistence states leray schauder degree email jfleck cict fr rpardo sunma4 mat ucm es

multiple solutions for an elliptic system near resonance abstract we consider an elliptic system with linear part depending on two parameters and a sublinear perturbation we obtain the existence of at least two solutions when the linear part is near resonance the system is associated with a strongly indefinite functional and the solutions are obtained through saddle point theorem and galerkin approximation

asymptotically periodic superquadratic hamiltonian systems abstract we obtain existence of solutions for the system u v x u f v x u v x r n v v x v f u x u v x r n where n 3 v c r n 0 is periodic and f c 1 r n r 2 r is superquadratic at infinity we consider the case that f is periodic and asymptotically periodic in the proofs we apply variational techniques

on the existence of many solutions for a class of superlinear elliptic systems abstract we seek multiple solutions to systems of semilinear elliptic equations of the type u x h x u x x u x 0 x where r n n 1 is a bounded regular domain and u u1 u2 r 2 for a class of potentials where the variables are strongly coupled as in the model h x u1 u2 u1 1 u2 2 with i 1 we provide the existence of nine nontrivial solutions characterized by sign properties of each component

existence and uniqueness of solutions for a singular semilinear elliptic system abstract in this paper we study the existence and the uniqueness of solutions for the singular semilinear elliptic system u f x u 2 g x u 1 p 2 p q a x u p v 1 q x r n v f x v 2 g x v 1 q 2 p q a x u 1 p v q x r n where 0 p 1 and 0 q 1 we show the existence of a solution for an approximated system by using a perturbation method which eliminates the singularity and via variational methods the limit of the approximated solutions is a positive solution in the case g 0 p q and 1 2 p 1 we prove the uniqueness of solution the proofs rely on the concentration compactness principle

symmetry and symmetry breaking for ground state solutions of some strongly coupled elliptic systems abstract we consider the ground state solutions of the lane emden system with henon type weights u x v q 1 v v x u p 1 u in the unit ball b of r n with dirichlet boundary conditions where n 1 0 p q 0 and 1 p 1 1 q 1 n 2 n we show that such ground state solutions u v always have definite sign in b and exhibit a foliated schwarz symmetry with respect to a unit vector of r n we also give precise conditions on the parameters p and q under which the ground state solutions are not radially symmetric

ground state solutions for a diffusion system in this paper we study the following diffusion system t u x u v x u g t x v t v x v v x v f t x u where z u v r r n r 2 v x c r n r is a general periodic function under weaker conditions on nonlinearity we establish the existence of ground state solutions via variational methods

the nehari manifold for indefinite semilinear elliptic systems involving critical exponent abstract in this paper we study the combined effect of concave and convex nonlinearities on the number of solutions for an indefinite semilinear elliptic system e involving critical exponents and sign changing weight functions using nehari manifold the system is proved to have at least two nontrivial nonnegative solutions when the pair of the parameters belongs to a certain subset of r 2

ground state solutions for superlinear elliptic systems on rn abstract this paper is concerned with the existence of the ground state solutions for the following superlinear elliptic system of hamiltonian type u v x u g x v in r n v v x v f x u in r n u x 0 and v x 0 as x where v c r n r is periodic in x 1 x 2 x n we assume that 0 lies in a gap of the spectrum v and f and g are both superlinear at 0 and infinity but they have different increasing rates at infinity by proving all cerami sequences for the energy functional are bounded existence of a ground state solution is obtained

a variational approach to subquadratic perturbations of elliptic systems abstract we consider subquadratic perturbations of semilinear elliptic systems which are in variational form a unified approach to both the cooperative and noncooperative problems is presented and a condition of nonquadraticity at infinity is introduced to treat the resonant cases through minimax techniques

decay symmetry and existence of solutions of semilinear elliptic systems our utmost aim was originally to establish the existence of solutions of system however in this effort we got sidetracked to consider other questions in this way we come to interesting results on asymptotic behavior of solutions on symmetry properties of such solutions and the existence of ground states

an infinite dimensional linking theorem and applications abstract in this paper we establish a new infinite dimensional linking theorem without ps type assumptions the new theorem needs a weaker linking geometry and produces bounded ps sequences the abstract result will be applied to the study of the existence of solutions of the strongly indefinite partial differential systems for the first application we consider the system u u in v v in u h v x u v on v h u x u v on where is a bounded domain in r n with smooth boundary is the outer normal derivative h r r r is a positive c 1 function one nontrivial solution is obtained the second application we will solve the eigenvalue problem of the system a v f x v w b w g x v w 0 where a b are self adjoint operators on l 2 r n is not necessarily bounded f g are caratheodory functions on r 2 we get infinitely many solutions we deal with asymptotically linear cases for both systems

nonequilibrium steady states of matrix product form a solver s guide we consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model among other things biological transport and traffic flow we begin with a broad overview of this class of driven diffusive systems which includes exclusion processes focusing on interesting physical properties such as shocks and phase transitions we then turn our attention specifically to those models for which the exact distribution of microstates in the steady state can be expressed in a matrix product form in addition to a gentle introduction to this matrix product approach how it works and how it relates to similar constructions that arise in other physical contexts we present a unified pedagogical account of the various means by which the statistical mechanical calculations of macroscopic physical quantities are actually performed we also review a number of more advanced topics including nonequilibrium free energy functionals the classification of exclusion processes involving multiple particle species existence proofs of a matrix product state for a given model and more complicated variants of the matrix product state that allow various types of parallel dynamics to be handled we conclude with a brief discussion of open problems for future research

lorentz sobolev spaces and systems of schrodinger equations in rn abstract we study the connection between the improvement of limiting sobolev s embeddings within the context of lorentz spaces and the variational approach to systems of nonlinear schrodinger equations we show that lorentz sobolev spaces appear as a natural function space domain for the related energy functional moreover in this framework the nonlinearity may exhibit a supercritical growth with respect to the maximal growth prescribed by the poho aev trudinger moser inequality and still preserving a variational structure

an existence result for a linear superlinear elliptic system with neumann boundary conditions abstract in this work we consider an elliptic system of two equations in dimension one with neumann boundary conditions where the nonlinearities are asymptotically linear at and superlinear at we obtain that under suitable hypotheses a solution exists for any couple of forcing terms in l 2 we also present a similar result in which the superlinearity is in only one of the two equations and we discuss the resonant problem too

solutions of a class of hamiltonian elliptic systems in rn we study the existence of ground state solutions for the following elliptic systems in rn u b xu u hv x u v v b xv v hu x u v where b b1 bn is a constant vector and h c1 rn r2 r is nonperiodic in variables x and super quadratic as z by a recent critical point theorem for strongly indefinite problem we obtain the existence of at least one ground state solution

strongly indefinite systems with critical sobolev exponents we consider an elliptic system of hamiltonian type on a bounded domain in the superlinear case with critical growth rates we obtain existence and positivity results for solutions under suitable conditions on the linear terms our proof is based on an adaptation of the dual variational method as applied before to the scalar case introduction existence and non existence of solutions of semilinear elliptic srstems has been a subject of active research recently see for example ff l3 ps such systems are called variational if solutions can be viewed as critical points of an associated functional defined on a suitable function space restricting our attention to systems with two unknowns we distinguish two classes of variational elliptic systems a potential systems b hamiltonian systems potential systems are of the form a llu u v ztl2v u v where l1 and l2 are second order selfadjoint elliptic operators formally these are the euler lagrange equations of the functional f u v l1u u i l2v v th u v here is the l2 inner product for functions defined on the underlying domain and tt u v s h u x v x dx the functional f is often called the lagrangian its critical points correspond to weak soltbtions of a the appropr ate choice of the function spaces for u and v follows by requiring that the quadratic part of f be well defined this naturally leads to sobolev spaces with square irltegrable first derivatives since also a must be well defined by virtue of the embedding theorems some growth restrictions on this latter function are required an extra difficulty appears if we consider system a with a plus sign in the second equation for then the corresponding functiorl f has a strongly indefinite quadratic part for systems of superlinear type and with sllbcritical growth the mountain pass theorem ar or in the strongly indefinite case the benci rabinowitz theorem received by the editors june 5 1996 1991 mathematics subject classification primary 35j50 35j55 35j65

existence and asymptotic behavior of ground states for schrodinger systems with hardy potential abstract in this paper we study the following schrodinger systems with hardy potential u u x 2 v f x z v x r n v v x 2 u f x z u x r n where z u v r 2 and r is a positive parameter this problem is related to coupled nonlinear schrodinger equations for bose einstein condensate under some suitable conditions on the parameter and nonlinearity f we first prove the existence exponential decay and convergence of ground state solutions via variational methods moreover we prove the monotonicity and convergence property of the energy of ground state solutions finally we also give the asymptotic behavior of ground state solutions as parameter tends to 0

critical growth fractional elliptic systems with exponential nonlinearity abstract we study the existence of positive solutions for the system of fractional elliptic equations of the type 1 2 u p p q f x u p 2 u v q h 1 u v e u 2 v 2 in 1 1 1 2 v q p q f x u p v q 2 v h 2 u v e u 2 v 2 in 1 1 u v 0 in 1 1 u v 0 in r 1 1 where 1 p q 2 h 1 u v 2 u 2 u 2 u v h 2 u v 2 v 2 u v 2 v and 2 here 1 2 is the fractional laplacian operator we show the existence of multiple solutions for suitable range of by analyzing the fibering maps and the corresponding nehari manifold we also study the existence of positive solutions for a superlinear system with critical growth exponential nonlinearity

ground state solutions of hamiltonian elliptic systems in dimension two the aim of this paper is to study hamiltonian elliptic system of the form 0 1 where 2 is a bounded domain in the second place we present existence results for the following stationary schrodinger systems defined in the whole plane 0 2 we assume that the nonlinearities f g have critical growth in the sense of trudinger moser by using a suitable variational framework based on the generalized nehari manifold method we obtain the existence of ground state solutions of both systems 0 1 and 0 2

the existence of solutions for superquadratic hamiltonian elliptic systems on rn abstract this paper is concerned with the following hamiltonian elliptic system u v x u h u x u v in r n v v x v h v x u v in r n u x 0 and v x 0 as x where v x c r n r and h x z is superquadratic in z as z with z u v by applying a critical point theorem for strongly indefinite functionals we obtain infinitely many solutions for the above system

finite size scaling and universality for the totally asymmetric simple exclusion process the applicability of the concepts of finite size scaling and universality to nonequilibrium phase transitions is considered in the framework of the one dimensional totally asymmetric simple exclusion process with open boundaries in the thermodynamic limit there are boundary induced transitions both of the first and second order between steady state phases of the model we derive finite size scaling expressions for the current near the continuous phase transition and for the local density near the first order transition under different stochastic dynamics and compare them to establish the existence of universal functions next we study numerically the finite size behavior of the lee yang zeros of the normalization factor for the different steady state probabilities

multiple positive solutions of nonhomogeneous elliptic systems with strongly indefinite structure and critical sobolev exponents abstract in this paper we study the existence of multiple positive solutions to some hamiltonian elliptic systems v u u p ef x u v v q g x in u v 0 in u v 0 on where is a bounded domain in r n n 3 0 f g l 1 p 1 1 q 1 n 2 n p q 1 0 using sub and supersolution method and based on an adaptation of the dual variational approach we prove the existence of at least two nontrivial positive solutions for all 0 1 and e 0 0 where 1 is the first eigenvalue of the laplace operator with zero dirichlet boundary conditions and 0 is a positive number

existence and multiplicity of semiclassical solutions for asymptotically hamiltonian elliptic systems abstract this paper is concerned with the following nonperiodic hamiltonian elliptic system e 2 u v x u h u x u v in r n e 2 v v x v h v x u v in r n u x 0 and v x 0 as x where e 0 is a small parameter and the potential v is bounded below and h is asymptotically linear in z as z with z u v by applying a generalized linking theorem of strongly indefinite functionals we obtain the existence of multiple semiclassical solutions for the above system

multiple solutions for asymptotically quadratic and superquadratic elliptic system of hamiltonian type this paper is concerned with the following nonperiodic hamiltonian elliptic system u v x u h v x u v x r n v v x v h u x u v x r n u x 0 v x 0 as x where z u v r n r i r n 3 and the potential v x is nonperiodic and sign changing by applying a generalized linking theorem for strongly indefinite functionals we establish the existence of multiple solutions for asymptotically quadratic nonlinearity as well as the existence of infinitely many solutions for superquadratic nonlinearity

existence of solutions for a class of noncooperative elliptic systems we establish the existence of a nontrivial solution for a class of noncooperative elliptic systems with nonlinearities of superlinear growth moreover if there is resonance we also find at least a solution all results are obtained by the minimax methods in critical point theory

on strongly indefinite systems involving the fractional laplacian abstract this paper is devoted to study strongly indefinite systems involving the fractional laplacian on bounded domains explicitly we obtain existence and non existence results a p r i o r i estimates of gidas spruck type and a symmetry result in addition we give a different proof for the a p r i o r i estimate for nonlinear elliptic problems with the fractional laplacian obtained in cabre and tan 2010 and tan 2013

existence and uniqueness of positive radial solutions for the lane emden system in this article we consider component wise positive radial solutions of a weakly coupled system of elliptic equations in a ball with homogeneous nonlinearities the existence is well known in general we give a result for the remaining cases the uniqueness is less studied we complement the known results

solutions of the mixed boundary problem and their morse indices abstract in this paper we study the solutions of the following mixed boundary problem u f x u in u 0 on 1 u 0 on 2 under some assumptions on the nonlinearity we will show that the boundedness of solutions is equivalent to the finiteness of their morse indices we extend the result of a bahri p l lions solutions of superlinear elliptic equations and their morse indices commun pure appl anal 45 1992 1205 1215 from the dirichlet boundary condition to the mixed boundary condition

existence of nonzero weak solutions for a class of elliptic variational inclusions systems in rn abstract we consider the following variational inclusions system of the form u u 1 f u v in r n v v 2 f u v in r n with u v h 1 r n where f r 2 r is a locally lipschitz function and i f u v i 1 2 are the partial generalized gradients in the sense of clarke under various growth conditions on the nonlinearity f we study the existence of nonzero weak solutions of the above system in the sense of hemivariational inequalities which are critical points of an appropriate locally lipschitz function defined on h 1 r n h 1 r n the main tool used in the paper is the principle of symmetric criticality for locally lipschitz functions

multiplicity for strongly indefinite semilinear elliptic system abstract in this paper we study a multiplicity result for a strongly indefinite semilinear elliptic system 2 u u g x v q 1 v in r n 2 v v f x u p 1 u in r n our interest is the relation between the number of solutions and the topology of the global minima set of a suitable ground energy function

liouville theorem for robin boundary value problems and finite morse indices in this paper we study the nonexistence result of the following nonlinear elliptic equation with robin boundary condition u u p 1uin r n u cu 0on r n under some assumptions on c and p we will show that this problem does not possess nontrivial bounded solution with finite morse index

existence of solutions for nonperiodic superquadratic hamiltonian elliptic systems abstract this paper is concerned with the following nonperiodic hamiltonian elliptic system u v x u r v x u v in r n v v x v r u x u v in r n u x 0 and v x 0 as x where r x z is superquadratic in z as z with z u v by applying a critical point theorem for strongly indefinite functionals we prove the existence of solution for the above system

multiple solutions of a coupled nonlinear schrodinger system abstract we will consider the relation between the number of positive standing waves solutions for a class of coupled nonlinear schrodinger system in r n and the topology of the set of minimum points of potential v x the main characteristics of the system are that its functional is strongly indefinite at zero and there is a lack of compactness in r n combining the dual variational method with the nehari technique and using the concentration compactness lemma we obtain the existence of multiple solutions associated to the set of global minimum points of the potential v x for sufficiently small in addition our result gives a partial answer to a problem raised by sirakov about existence of solutions of the perturbed system

on a superquadratic elliptic system with strongly indefinite structure abstract in this paper we consider the elliptic system u g x v in v f x u in u v 0 on where is a bounded smooth domain in r n and f and g satisfy a general superquadratic condition by using variational methods we prove the existence of infinitely many solutions our argument relies on the application of a generalized variant fountain theorem for strongly indefinite functionals previous results in the topic are improved

differential systems with strongly indefinite variational structure abstract the euler lagrange equations of lagrangians with a strongly indefinite quadratic part are studied by means of the direct min max method of benci and rabinowitz the simplest case is a system of two coupled semilinear poisson equations using an analytic framework of a suitable family of products of fractional sobolev spaces existence results are obtained for all nonlinearities with subcritical growth rates

strongly indefinite functionals and multiple solutions of elliptic systems we study existence and multiplicity of solutions of the elliptic system left begin array 20 l updelta u h u x u v hfill text in upomega hfill updelta v h v x u v hfill text in upomega quad u x v x 0 quad text on partial upomega hfill end array right where upomega subset mathbb r n n ge 3 is a smooth bounded domain and h in mathcal c 1 overline upomega times mathbb r 2 mathbb r we assume that the nonlinear term h x u v sim left u right p left v right q r x u v text with mathop lim limits left u v right to infty frac r x u v left u right p left v right q 0 where p in 1 2 2 2n n 2 text and q in 1 infty so some supercritical systems are included nontrivial solutions are obtained when h x u v is even in u v we show that the system possesses a sequence of solutions associated with a sequence of positive energies resp negative energies going toward infinity resp zero if p 2 resp p 2 all results are proved using variational methods some new critical point theorems for strongly indefinite functionals are proved

asymptotically linear elliptic systems in rn abstract in this paper we show that semilinear elliptic systems of the form u u v v g v v v u u f u x r n possess at least one nontrivial solution pair u v h 1 r n h 1 r n where and are positive numbers f t and g t are continuous functions on r and asymptotically linear as t

exact results for a fully asymmetric exclusion process with sequential dynamics and open boundaries an exact and rigorous calculation of the current and density profile in the steady state of the one dimensional fully asymmetric simple exclusion process with open boundaries and forward ordered sequential dynamics is presented the method is based on a matrix product representation of the steady state probability distribution the main idea is to choose a suitable representation in which the scalar products describing the current and local density profile for a chain of arbitrary finite size depend only on the elements in a finite number of rows and columns this makes possible the use of a truncated finite dimensional representation of the matrices and vectors involved after performing the calculations we lift the truncation by letting its dimensionality go to infinity in this limit the results become exact for any size of the chain by rescaling one of the infinitedimensional matrix representations found in the work of derrida et al j phys a 26 1493 1993 for their algebra we obtain a symmetric propagator matrix its truncated version is diagonalized by orthogonal transformation for easy calculation of the relevant scalar products an interpretation of the phase transitions between the different phases is given in terms of eigenvalue splitting from a bounded quasicontinuous spectrum a precise description of the local density profiles is given for all values of the parameters it is shown that the leading order asymptotic form of the position dependent terms in the local density changes within the low and high density phases signaling the presence of a higher order transition