Mediterranean Journal of Mathematics   2016 年 13 卷 5 期

2016.10.01

In this paper, we study the existence of infinitely many homoclinic solutions of the perturbed second-order Hamiltonian system (Formula Presented.), where L(t) and W(t, u) are neither autonomous nor periodic in t. Under the assumptions that W(t, u) is indefinite in sign and only locally superquadratic as |u| ??’ + ??? and G(t, u) is not even in u, we prove the existence of infinitely many homoclinic solutions in spite of the lack of the symmetry of this problem by Bolle???s perturbation method in critical point theory. Our results generalize some known results and are even new in the symmetric case.