Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 197, pp. 1-14.

Title: Subharmonic solutions for first-order Hamiltonian systems

Author: Mohsen Timoumi (Faculty of Sciences, Tunisia)

Abstract:
 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.

Submitted March 31, 2013. Published September 05, 2013.
Math Subject Classifications: 34C25.
Key Words: Hamiltonian systems; periodic solutions; subharmonic;
           minimal periods; generalized saddle point theorem.