Existence of homoclinic solutions for second order Hamiltonian systems with general potentials

In this paper we are concerned with the existence of homoclinic solutions for the following second order non-autonomous Hamiltonian systems q̈ -L(t)q+W-{q}(t,q)=0, where W ε C1 (ℝ × ℝn, ℝ) and L ε C(ℝ, ℝn2 is a symmetric and positive definite matrix for all t ε ℝ. Assuming that the potential W satisfies some weaken global Ambrosetti-Rabinowitz conditions and L meets the coercive condition, we show that (HS) has at least one nontrivial homoclinic solution via using the Mountain Pass Theorem. Some recent results in the literature are generalized and significantly improved. © 2013 Korean Society for Computational and Applied Mathematics.