the unregularized gradient flow of the symplectic action the symplectic action can be defined on the space of smooth paths in a symplectic manifold p which join two lagrangian submanifolds of p to pursue a new approach to the variational theory of this function we define on a subset of the path space the flow whose trajectories are given by the solutions of the cauchy riemann equation with respect to a suitable almost complex structure on p in particular we prove compactness and transversality results for the set of bounded trajectories

a variational construction of chaotic trajectories for a reversible hamiltonian system abstract a geometric criterion for the existence of chaotic trajectories of a reversible hamiltonian system with the configuration space t n with n a compact manifold is given the main result is a variational version of the theorem of d v turayev and l p shilnikov dokl akad nauk sssr 304 1989 811 814 on the symbolic representation of trajectories of hamiltonian systems possessing several homoclinics to a saddle equilibrium

on some existence and uniqueness results in contact problems with nonlocal friction the workwe present is a mathematical study of signorini s problem with friction i e the problem of equilibrium of a linearly elastic body in contact with a rigid foundation until recently the questions of existence and uniqueness of solutions to such problems were open recently two ideas have appeared which have led to some positive results the first presented by netas jarusek haslinger 11 involves a concept of small friction and provides for the development of an existence result for a very special case of a uniformly loaded infinite strip the second established by duvaut 5 is based on the idea of a nonlocal friction law which enables one to establish an existence result for any friction and also to establish uniqueness for small friction in this paper we present some new results in this direction and a new proof of a non local existence theory our approach differs considerably from the proof outlined in 5 instead of using fixed point arguments we develop a theory of perturbed variational inequalities the origin of which can be found in 9 and establish a generalization for the class of nonlinear variational inequalities characterizing the non local signorini problem this approach should prove to be very useful in studies of approximations of friction prohlems

homoclinic orbits for second order hamiltonian systems possessing superquadratic potentials received by the editors november 27 1990 1991 mathematics subject classification primary 34c99 58e99 58f99 the first author was supported by ministero p i gruppo 40 calcolo delle variazioni the second author s research was sponsored in part by the u s army research office under contract daal03 87 k 0043 the national science foundation under grant mcs 8110556 and the office of naval research under grant n00014 88 ko134 any reproduction for the purpose of the united states govemment is permitted

numerical simulation of some variational inequalities arisen from unilateral contact problems by the finite element methods this contribution deals with the finite element approximation of the variational inequalities coming from the signorini problem and the unilateral contact between two elastic bodies the numerical analysis we carry out improves former results and states optimal convergence rates under reasonable regularity hypotheses for both conforming and nonconforming methods

homoclinic orbits on compact manifolds abstract under a suitable assumption on the potential energy v we prove the existence of a homoclinic orbit of the equation dt x t grad v x t 0 x m where m is a compact riemannian manifold our assumption is satisfied for instance if the function v has a unique nondegenerate maximum point

two results on solution uniqueness and multiplicity for the linear elastic friction problem with normal compliance abstract this study is concerned with the frictional contact problem governed by the normal compliance law in linear elasticity the paper presents two contributions dealing with the stationary problem we first obtain improved bounds ensuring the uniqueness of a solution second we exhibit examples in which infinitely many solutions to the problem exist

quasistatic normal compliance contact problem of visco elastic bodies with coulomb friction implemented by qp and sgbem the quasistatic normal compliance contact problem of isotropic homogeneous linear visco elastic bodies with coulomb friction at small strains in kelvin voigt rheology is considered the discretization is made by a semi implicit formula in time and the symmetric galerkin boundary element method sgbem in space assuming that the ratio of the viscosity and elasticity moduli is a given relaxation time coefficient the obtained recursive minimization problem formulated only on the contact boundary has a nonsmooth cost function if the normal compliance responds linearly and the 2d problems are considered then the cost function is piecewise quadratic which after a certain transformation gets the quadratic programming qp structure however it would lead to second order cone programming in 3d problems finally several computational tests are presented and analysed with an additional discussion on numerical stability and convergence of the involved approximated poincare steklov operators

genericity of the multibump dynamics for almost periodic duffing like systems in this paper we consider slowly oscillating perturbations of almost periodic du ng like systems i e systems of the form u u a t t w0 u t r u rn where w c2n rn r is superquadratic and a and are positive and almost periodic by variational methods we prove that if 0 is small enough then the system admits a multibump dynamics as a corollary we get that the system u u a t w0 u t r u rn admits multibump solutions whenever a a where a is an open dense subset of a c r r a is almost periodic and a t 0 t r

a quasistatic frictional problem with normal compliance a friction and contact problem will be considered for an elastic solid body which under the influence of volume and surface forces is in contact with a rigid foundation

on solution multiplicity in friction problems with normal compliance this work is concerned with the normal compliance model and friction in linear elastostatics we consider the two dimensional sliding problem and we seek those interface parameters leading to infinitely many solutions of the continuous and the finite element discretized problem the determination of the interface parameters uses a specific eigenvalue problem in the discrete case the framework is illustrated with an elementary example and some finite element computations

first order elliptic systems and the existence of homoclinic orbits in hamiltonian systems and h r x r 2 r is smooth by a homoclinic or a doubly asymptotic orbit to y where y is a periodic solution of 1 we mean a solution x y of 1 such that i x 0 y t l 0 as i tl oo finding homoclinic orbits in systems like 1 can be quite difficult in the case when y is a hyperbolic orbit this is equivalent to showing that the stable and unstable manifold of y intersect in some situation this can be done by melnikov s method recently some progress has been made by applying variational methods coti zelati and ekeland showed in 3 using dual variational methods that 1 has at least one homoclinic orbit if h satisfies some convexity and growth assumptions in their proof the convexity assumption enters in a crucial way already in the set up of the variational problem variational methods have been used by benci and giannoni 2 who studied homoclinic orbits on compact riemannian manifolds and by p rabinowitz in 9 who proved existence of heteroclinic orbits on the n dimensional torus as well as their multiplicity in 2 and 9 only special hamiltonian of lagrangian type are studied the associated variational problem is then at least semi definite the

homoclinics and heteroclinics for a class of conservative singular hamiltonian systems abstract we consider an autonomous hamiltonian system u v u 0 where the potential v r 2 r has a strict global maximum at the origin and a singularity at some point 0 under some compactness conditions on v at infinity and around the singularity we study the existence of homoclinic orbits to 0 winding around we use a sufficient and in some sense necessary geometrical condition on v to prove the existence of infinitely many homoclinics each one being characterized by a distinct winding number around moreover under the condition there exists a minimal non contractible periodic orbit and we establish the existence of a heteroclinic orbit from 0 to this connecting orbit is obtained as the limit in the c 1 loc topology of a sequence of homoclinics with a winding number larger and larger