Existence and Multiplicity of Homoclinic Solutions for the Second Order Hamiltonian systems

In this paper we study the existence and multiplicity of homoclinic solutions for the second order Hamiltonian system ü−L(t)u(t)+Wu(t, u) = 0, ∀t ∈ R, by means of the minmax arguments in the critical point the-ory, where L(t) is unnecessary uniformly positively definite for all t ∈ R and Wu(t, u) sastisfies the asymptotically linear condition