Homoclinic solutions for a class of the second order Hamiltonian systems

We study the existence of homoclinic orbits for the second order Hamiltonian system <(q)double over dot > + V-q (t, q) = f (t), where q is an element of R-n and V is an element of C-1 (R x R-n, R), V(t, q)=- K (t, q) + W(t, q) is T-periodic in t. A map K satisfies the "pinching" condition b(1)vertical bar q vertical bar(2) <= K (t, q) <= b(2) vertical bar q vertical bar(2), W is superlinear at the infinity and f is sufficiently small in L-2(R, R-n). A homoclinic orbit is obtained as a limit of 2kT-periodic solutions of a certain sequence of the second order differential equations. (c) 2005 Elsevier Inc. All rights reserved.