Homoclinic solutions for a class of non-autonomous subquadratic second-order Hamiltonian systems

In this paper we consider the existence of homoclinic solutions for the following second-order non-autonomous Hamiltonian system: q - L(t)q + W-q(t,q) = 0, (HS) where L(t) is an element of C(R, R-n2) is a symmetric and positive definite matrix for all t is an element of R, W(t, q) = a(t)|q|(gamma) with a(t) : R -> R+ is a positive continuous function and 1 < gamma < 2 is a constant. Adopting some other reasonable assumptions for L and W, we obtain a new criterion for guaranteeing that (HS) has one nontrivial homoclinic solution by use of a standard minimizing argument in critical point theory. Recent results from the literature are generalized and significantly improved. (C) 2009 Elsevier Ltd. All rights reserved.