Periodic solutions for second order Hamiltonian systems with general superquadratic potential

Abstract

In this paper, we study the existence of nontrivial solutions and ground state solutions for the second order Hamiltonian systems: $$ \ddot u(t)+A(t)u(t)+\nabla F(t,u(t))=0\ \ \ \ \ \ \mbox{a.e. } t\in [0,T], $$ where $A(t)$ is a $N\times N$ symmetric matrix, continuous and $T$-periodic in $t$. Replacing the classical Ambrosetti-Rabinowitz superquadratic condition by a general superquadratic condition, we prove some existence theorems, which unify and improve some recent results in the literature.