Multiple Homoclinic Solutions for Second‐Order Perturbed Hamiltonian Systems. Issue 2 (25th June 2013) - Ye, Yiwei
Abstract In this paper, we study the second‐order perturbed Hamiltonian systems ü(t)−λL(t)u(t)+∇W(t, u(t))=f(t), where λ≥1 is a parameter, L(t) is positive definite for all t∈R but unnecessarily uniformly positive definite for t∈R, and W is either asymptotically quadratic or superquadratic in x as |x|→∞. Based on variational methods, we prove the existence of at least two nontrivial homoclinic solutions for the above system when f∈L2(R, RN)∖0 small enough.