Existence of homoclinic solution for the second order Hamiltonian systems

An existence theorem of homoclinic solution is obtained for a class of the nonautonomous second order Hamiltonian systems (u) double over dot(t) - L(t)u(t) + delW(t, u(t)) = 0, For Allt is an element of R, by the minimax methods in the critical point theory, specially, the generalized mountain pass theorem, where L(t) is unnecessary uniformly positively definite for all t is an element of R, and W(t, x) satisfies the superquadratic condition W(t,x)/\x\(2) --> + infinity as \x\ --> infinity uniformly in t, and need not satisfy the global Ambrosetti-Rabinowitz condition. (C) 2003 Elsevier Inc. All rights reserved.