Electron. J. Diff. Equ., Vol. 2013 (2013), No. 197, pp. 1-14.

Subharmonic solutions for first-order Hamiltonian systems

Mohsen Timoumi

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 5, 2013.
Math Subject Classifications: 34C25.
Key Words: Hamiltonian systems; periodic solutions; subharmonic; minimal periods; generalized 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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