Homoclinic solutions for a class of the second order Hamiltonian systems

Abstract

We study the existence of homoclinic orbits for the second order Hamiltonian system q̈ + Vq(t, q) = f(t), where q ∈ ℝn and V ∈ C1(ℝxℝn, ℝ), V(t, q) = -K(t, q) + W(t, q) is T-periodic in t. A map K satisfies the "pinching" condition b1 q 2 ≤ K(t, q) ≤ b2 q2, W is superlinear at the infinity and f is sufficiently small in L2,(ℝ, ℝn). A homoclinic orbit is obtained as a limit of 2kT-periodic solutions of a certain sequence of the second order differential equations. © 2005 Elsevier Inc. All rights reserved.