Existence of homoclinic orbits for asymptotically periodic systems involving Duffing-like equation

Abstract

We are concerned with perturbations of the Hamiltonian system of the type q̈-L(t)(q)+W(q)(t,q)=0, t ε R, where q = (q 1,⋯, q N) ε R N, W ε C 1 (R × R N, R), and L(t) ε C (R, R N2) is a positive definite symmetric matrix. Variational arguments are used to prove the existence of homoclinic solutions for system (HS). © 2003 Elsevier Science Ltd. All rights reserved.