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% "Ca1co10 delle variazioniâ€¦ (More)

In this paper we introduce an integer-valued degree for second order fully nonlinear elliptic operators with nonlinear oblique boundary conditions. We also give some applications to the existence ofâ€¦ (More)

This paper uses variational methods to establish the existence of so-called multi-bump homoclinic solutions for a family of singular Hamiltonian systems in R 2 which are subjected to almost periodicâ€¦ (More)

An S version of the Borsuk-Ulam Theorem is proved for a situation where Fix S I may be nontrivial. The proof is accomplished with the aid of a new relative index theory. Applications are given toâ€¦ (More)

where a and W satisfy (a1) a(t) is a continuous almost periodic function of t with a(t) â‰¥ a0 > 0 for all t âˆˆ R. (W1) There is a Î¾ âˆˆ R\{0} such that W âˆˆ C(R\{Î¾}, R). (W2) limxâ†’Î¾ W (x) = âˆ’âˆž. (W3) Thereâ€¦ (More)

We extend some earlier results on existence of homoclinic solutions for a class of Hamiltonian systems. We also study heteroclinic solutions. We use variational approach.

In this study, we study a Kirchhoff type problem involving singular and critical nonlinearities. With aid of variational methods and concentration compactness principle, we prove that the problemâ€¦ (More)

Proceedings of the National Academy of Sciencesâ€¦

1999

A Lagrangian system on 2 that has been studied earlier under a geometrical condition and found to possess a pair of solutions, H+/-, homoclinic to periodic solutions, v+/-, of a given homotopy type,â€¦ (More)