Periodic solutions of classical Hamiltonian systems without Palais-Smale condition

Guihua Fei; Soon Kyu Kim; Tixiang Wang

doi:10.1006/jmaa.2001.7802

Periodic solutions of classical Hamiltonian systems without Palais-Smale condition

Guihua Fei, Soon Kyu Kim, Tixiang Wang

Mathematics & Statistics

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Abstract

In this paper, we study the existence of periodic solutions for classical Hamiltonian systems without the Palais-Smale condition. We prove that the information of the potential function contained in a finite domain is sufficient for the existence of periodic solutions. Moreover, we establish the existence of infinitely many periodic solutions without any symmetric condition on the potential function V.

Original language	English (US)
Pages (from-to)	665-678
Number of pages	14
Journal	Journal of Mathematical Analysis and Applications
Volume	267
Issue number	2
DOIs	https://doi.org/10.1006/jmaa.2001.7802
State	Published - Mar 15 2002

Keywords

Classical Hamiltonian systems
Conley index
Galerkin approximation
Period solutions

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AU - Fei, Guihua

AU - Kim, Soon Kyu

AU - Wang, Tixiang

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N2 - In this paper, we study the existence of periodic solutions for classical Hamiltonian systems without the Palais-Smale condition. We prove that the information of the potential function contained in a finite domain is sufficient for the existence of periodic solutions. Moreover, we establish the existence of infinitely many periodic solutions without any symmetric condition on the potential function V.

AB - In this paper, we study the existence of periodic solutions for classical Hamiltonian systems without the Palais-Smale condition. We prove that the information of the potential function contained in a finite domain is sufficient for the existence of periodic solutions. Moreover, we establish the existence of infinitely many periodic solutions without any symmetric condition on the potential function V.

KW - Classical Hamiltonian systems

KW - Conley index

KW - Galerkin approximation

KW - Period solutions

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Periodic solutions of classical Hamiltonian systems without Palais-Smale condition

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