Electron. J. Diff. Equ., Vol. 2012 (2012), No. 178, pp. 1-12.

Subharmonic solutions for nonautonomous second-order Hamiltonian systems

Mohsen Timoumi

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.

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Mohsen Timoumi
Department of Mathematics, Faculty of Sciences
5000 Monastir, Tunisia
email: m_timoumi@yahoo.com

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