Existence of Solutions for Second-Order Hamiltonian Systems with Resonance

Abstract

In 2014, J. Pipan and M. Schechter discussed periodic solutions for second-order Hamiltonian systems with resonance. In this paper, we will generalize their results. To this end, we will first establish an index theory for second-order linear Hamiltonian systems with coefficient matrix in $$L^1$$. Then we propose generalized assumptions. We also investigate multiple solutions for symmetric second-order Hamiltonian systems.