Periodic solutions of second order Hamiltonian systems with nonlinearity of general linear growth

Abstract

In this paper we consider a class of second order Hamiltonian system with the nonlinearity of linear growth. Compared with the existing results, we do not assume an asymptotic of the nonlinearity at infinity to exist. Moreover, we allow the system to be resonant at zero. Under some general conditions, we will establish the existence and multiplicity of nontrivial periodic solutions by using the Morse theory and two critical point theorems.

Keywords

• second order hamiltonian systems
• periodic solutions
• morse theory
• critical groups