Periodic and subharmonic solutions for a class of superquadratic second order Hamiltonian systems (Q1030122)

The paper is concerned with second order Hamiltonian systems of the form \(\ddot{u}+A(t) u+\nabla F(t,u)=0\) in \(\mathbb{R}^N\). Here \(A(t)\) is a symmetric \(N\times N\) matrix, and both \(A\) and \(F\) are \(T\)-periodic in \(t\). The authors prove the existence of a \(T\)-periodic solution and of subharmonic solutions under various additional conditions on \(A\) and \(F\). The proof is based on standard variational methods.