Two Almost Homoclinic Solutions for a Class of Perturbed Hamiltonian Systems Without Coercive Conditions - Zhang, Ziheng; Yuan, Rong (Mathematical Modelling and Analysis, 2015)
In this paper we consider the existence of almost homoclinic solutions for the following second order perturbed Hamiltonian systems  ü- L(t)u + ∇W (t, u) = f (t), (PHS)  where  is a symmetric and positive definite matrix for all t ∈ R, W ∈ C1(R×Rn, R) and ∇W (t, u) is the gradient of W (t, u) at u, f ∈ C(R, Rn) and belongs to L2(R, Rn). The novelty of this paper is that, assuming L(t) is bounded in the sense that there are two constants 0