Solutions of minimal period for a Hamiltonian system with a changing sign potential

Yavdat Il'yasov; Nadir Sari

doi:10.3934/cpaa.2005.4.175

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2005, Volume 4, Issue 1: 175-185. Doi: 10.3934/cpaa.2005.4.175

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Solutions of minimal period for a Hamiltonian system with a changing sign potential

Yavdat Il'yasov^1, and
Nadir Sari^1,

1.
Laboratoire de Mathématiques et Applications, Université de La Rochelle, 17042 La Rochelle

Received: January 31, 2004

Revised: July 31, 2004

Published: February 2005

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Abstract

We consider a class of second-order Hamiltonian systems with a potential indefinite in sign. Applying the fibering approach we prove some existence and multiplicity results of periodic solutions with minimal period. We also give an answer to the problem of the existence of solutions with prescribed period $T$ which is greater than the first eigenvalue $\frac{2\pi}{\omega_n}$ of the corresponding linear problem.

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Mathematics Subject Classification: 34C25, 34B15, 34C23, 58E05.

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