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March  2005, 4(1): 175-185. doi: 10.3934/cpaa.2005.4.175

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, France, France

Received  February 2004 Revised  August 2004 Published  December 2004

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.
Keywords: indefinite potential, Palais- Smale condition, variational methods, Lusternik-Schnirelman theory., Periodic solution.
Mathematics Subject Classification: 34C25, 34B15, 34C23, 58E0.
Citation: Yavdat Il'yasov, Nadir Sari. Solutions of minimal period for a Hamiltonian system with a changing sign potential. Communications on Pure and Applied Analysis, 2005, 4 (1) : 175-185. doi: 10.3934/cpaa.2005.4.175
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