an avoiding cones condition for the poincare birkhoff theorem abstract we provide a geometric assumption which unifies and generalizes the conditions proposed in 11 12 so to obtain a higher dimensional version of the poincare birkhoff fixed point theorem for poincare maps of hamiltonian systems

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

critical point theory for nonsmooth functionals abstract in this paper we develop critical point theory for nonsmooth functional f h 0 1 r defined by f u 1 2 i j 1 a i j x u d i u d j u d x g x u d x the corresponding deformation lemmas are proved with the application to the bifurcation for quasilinear schrodinger equations in mind we extend the obtained results to that for a functional defined on a product space and prove a generalized saddle point theorem

abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity critical point theorems and applications to some nonlinear problems with strong resonance at infinity p bartolo and v benci istituto di matematica applicata via re david x0 bari ital and istituto di analisi matematica palazzo ateneo l ia scolai 2 bari italy received in revised form 20 december 1952

interpolation and sampling hypersurfaces for the bargmann fock space in higher dimensions we study those smooth complex hypersurfaces w in open image in new window having the property that all holomorphic functions of finite weighted lp norm on w extend to entire functions with finite weighted lp norm such hypersurfaces are called interpolation hypersurfaces we also examine the dual problem of finding all sampling hypersurfaces i e smooth hypersurfaces w in open image in new window such that any entire function with finite weighted lp norm is stably determined by its restriction to w

multiple solutions of hamiltonian systems via limit relative category by means of an extension of relative category we prove by a linking type theorem the existence of two distinct critical levels for a strongly indefinite functional applications to asymptotically linear hamiltonian systems are given

integral formulas and an explicit version of the fundamental principle soit p c n c m une application polynomiale et on considere le systeme d equations differentielles p j d f t 0 j 1 m ou d i t et f est une fonction lisse dans un domaine convexe borne r n on presente une version explicite qui emploie des formules integrales et des courants residus du principe fondamental de ehrenpreis et palamodov

a boundary element method for steady incompressible thermoviscous flow a boundary element formulation is presented for moderate reynolds number steady incompressible thermoviscous flows the governing integral equations are written exclusively in terms of velocities and temperatures thus eliminating the need for the computation of any gradients furthermore with the introduction of reference velocities and temperatures volume modelling can often be confined to only a small portion of the problem domain typically near obstacles or walls the numerical implementation includes higher order elements adaptive integration and multiregion capability both the integral formulation and implementation are discussed in detail several examples illustrate the high level of accuracy that is obtainable with the current method

bifurcations for quasilinear schrodinger equations i abstract this paper is concerned with bifurcation problems for quasilinear schrodinger type equations such as the modified nonlinear schrodinger equations which have appeared as several models from mathematical physics we give a new approach for dealing with bifurcation problems of nonlinear potential operators the novelty of our approach lies in establishing multiple bifurcations without making a reduction to finite dimensional problems the finite dimensional reduction procedures that have been used in the past work for semilinear problems but are not suitable for quasilinear problems we give a unified approach requiring much less regularity of the problems as applications we provide multiple bifurcation results for the modified nonlinear schrodinger equations

rotation type solutions for spatially periodic hamiltonian systems along with solutions of 0 2 and in general for o l the hamiltonian h also called the energy is conserved this one dimensional situation can be studied in the phase space that is r x s since the sine function is periodic when the energy his prescribed and bigger than 1 then system 0 2 has two periodic solutions these periodic solutions however are not homotopic to a constant and they are usually called rotation type solutions it is the purpose of this paper to generalize this situation to equation 0 1 spatially periodic hamiltonian systems have been studied by several authors the nonautonomous case of 0 1 has been considered in l 7 for the existence of periodic solutions see also references therein the papers of liu s and the author 3 are specially related to this work there the existence of periodic solutions is established through a generalized saddle point theorem the hypotheses on h assumed in 3 will be considered here

periodic solutions for some nonautonomous second order hamiltonian systems the existence and multiplicity of periodic solutions are obtained for nonautonomous second order hamiltonian systems by the minimax methods in critical point theory

multiple periodic solutions for second order discrete hamiltonian systems some existence and multiplicity results are obtained for periodic solutions of nonautonomous second order discrete hamiltonian systems with partially periodic potentials by using critical point theory

division formulas on projective varieties we introduce a division formula on a possibly singular projective subvariety x of complex projective space mathbb p n which e g provides explicit representations of solutions to various polynomial division problems on the affine part of x especially we consider a global effective version of the briancon skoda huneke theorem

a generalized saddle point theorem abstract the well known saddle point theorem is extended to the case of functions defined on a product space x v where x is a banach space and v is a compact manifold under some linking conditions the existence of at least cuplength v 1 critical points is proved the abstract theorems are applied to the existence problems of periodic solutions of hamiltonian systems with periodic nonlinearity and or resonance

a boundary value problem with a periodic nonlinearity soit g r r une fonction continue et periodique de periode t 0 et soit h l 1 0 on considere le probleme d existence pour le probleme aux limites de picard u u g u h u 0 0 u

on a notion of category depending on a functional part ii an application to hamiltonian systems abstract we apply the notion of limit relative category depending on a functional f introduced in beauchemin and frigon 2009 16 to establish the existence of multiple periodic solutions to a hamiltonian system with periodic nonlinearity and superquadratic growth in some spatial variables

periodic solutions to differential systems with unbounded or periodic nonlinearities we investigate the existence of multiple solutions of differential systems of josephson type with unbounded or periodic nonlinearities some new results are obtained and some results in the literature are improved

a note on a resonance problem in this paper we prove the existence of at least one solution to the problem where k is an eigenvalue of the linear part h is orthogonal to the eigenspace corresponding to r and g is a nonlinear perturbation which can be for instance a continuous periodic real function with mean value zero we employ the techniques used by the second author in a previous paper in which the same result was obtained in the case in which r is assumed to be simple the final result is obtained by using variational methods and in particular a suitable version of the saddle point theorem of p rabinowitz

some critical point theorems and their applications to periodic solution for second order hamiltonian systems abstract some critical point theorems without the compactness assumptions are obtained by the reduction method the perturbation argument and the least action principle as applications some existence results of periodic solutions are obtained for nonautonomous second order hamiltonian systems which unify and generalize some recent corresponding results

periodic solutions of spatially periodic hamiltonian systems abstract this work is concerned with the study of existence and multiplicity of periodic solutions of hamiltonian systems of ordinary differential equations z j hz z t f t when the hamiltonian h z t h p q t is periodic in the variable q and superlinear in the variable p by imposing a growth condition on the derivative of h we obtain the existence of at least n 1 periodic solutions where n is the dimension of the system the existence of periodic solutions is obtained by using a saddle point theorem recently proved by lui we consider a functional over e x m where e is a hilbert space and m is a compact manifold satisfying a saddle point condition on e uniformly on m we present a proof of this saddle point theorem using standard minimax techniques based on the cup length of m

a time marching integral equation method for unsteady state problems abstract a time marching integral equation method is developed for solving three classes of differential equations elliptic hyperbolic and parabolic with the elliptic equation as the steady state limiting case of hyperbolic or parabolic equations the method described is semi analytical with its numerical aspect in the time discretization of the differential equation and the space discretization of the integral equation and its analytical aspect in the derivation of the integral equation via the green s function method the analyses of the time marching integral equation for three limiting cases indicate that both the steady integral equation and the explicit algorithm are special cases of the time marching integral equation finite element ideas have been used to discretize the derived integral equations some physical problems are analysed to illustrate the method and demonstrate its reliability and efficiency

periodic solutions for nonautonomous second order systems with bounded nonlinearity some existence and multiplicity theorems are obtained for periodic solutions of nonautonomous second order systems with bounded nonlinearity by the minimax methods

explicit representation of membership in polynomial ideals we introduce a new division formula on projective space which provides explicit solutions to various polynomial division problems with sharp degree estimates we consider simple examples as the classical macaulay theorem as well as a quite recent result by hickel related to the effective nullstellensatz we also obtain a related result that generalizes max noether s classical af bg theorem

a time marching boundary element method for two dimensional incompressible thermally coupled flows abstract a time marching boundary element method is developed for the solution of two dimensional incompressible thermally coupled flows by applying the operator splitting technique and time difference discretization semi discretized semi implicit differential equations are obtained and then green s function method is used to derive time marching integral equations and time marching boundary integral equations the relation between the time marching boundary integral equation and an explicit time integration scheme is brought to light the boundary element and finite element approaches are employed to solve the resulting time marching boundary integral equations numerical calculations have been carried out for the free convection flow in a unit square cavity for testing the accuracy and efficiency of the present method

boundary element methods for transient convective diffusion part i general formulation and 1d implementation a general formulation of higher order boundary element methods bem is presented for time dependent convective diffusion problems in one and multi dimensions free space time dependent convective diffusion fundamental solutions originally proposed by carslaw and jaeger are used to obtain the boundary integral formulation linear quadratic and quartic time interpolation functions are introduced in this paper for approximate representation of time dependent boundary temperatures and normal fluxes closed form time integration of the kernels is mandatory to attain both accuracy and efficiency of the numerical approach a complete set of time integrals for the one dimensional formulation is presented here for the first time in the literature