Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 178, pp. 1-12.

Title: Subharmonic solutions for nonautonomous
       second-order Hamiltonian systems
 
Author: Mohsen Timoumi (Faculty of Sciences, Tunisia)

Abstract:
 In this article, we prove the existence of subharmonic solutions for
 the non-autonomous second-order Hamiltonian system 
 $\ddot{u}(t)+V'(t,u(t))=0$.
 Also we study the minimality of their periods, when the nonlinearity
 $V'(t,x)$ grows faster than   $|x|^{\alpha}$, $\alpha\in[0,1[$ 
 at infinity.  The proof is based on the Least Action Principle 
 and the Saddle Point Theorem.
 
Submitted March 9, 2012. Published October 12, 2012.
Math Subject Classifications: 34C25.
Key Words: Hamiltonian systems; subharmonics; minimal periods;
           saddle point theorem.