Subharmonic solutions for first-order Hamiltonian systems

In this article, we study the existence of periodic and subharmonic solutions for a class of non-autonomous first-order Hamiltonian systems such that the nonlinearity has a growth at infinity faster than $|x|^{\alpha}$, $0\leq\alpha < 1$. We also study the minimality of periods for such solutions. Our results are illustrated by specific examples. The proofs are based on the least action principle and a generalized saddle point theorem.