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: equation(HS)q̈−L(t)q+Wq(t,q)=0, where L(t)∈C(R,Rn2)L(t)∈C(R,Rn2) is a symmetric and positive definite matrix for all t∈Rt∈R, W(t,q)=a(t)|q|γW(t,q)=a(t)|q|γ with a(t):R→R+a(t):R→R+ is a positive continuous function and 1<γ<21<γ<2 is a constant. Adopting some other reasonable assumptions for LL and WW, 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.