MULTIPLE HOMOCLINICS FOR A CLASS OF SINGULAR HAMILTONIAN-SYSTEMS

We consider a Hamiltonian system u + del V(u) = 0 where the potential V: R-N\S --> R has a unique strict global maximum at a point p is an e lement of R-N and a singular set S subset of RN\{p} such that R-N\S is open, path-connected and the fundamental group G = pi(1)(R-N\S) is no ntrivial. Under some compactness conditions on V at infinity and aroun d the singular set S we study the existence of homoclinic orbits to p which link with S. When V and G satisfy suitable geometrical condition s, we can prove the existence of multiple homoclinics, each one belong ing to a different homotopy class of G. (C) 1997 Academic Press.