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Subharmonics near an equilibrium for some second-order Hamiltonian systems

Published online by Cambridge University Press:  14 November 2011

Patricio L. Felmer  and
Elves A. de B. e Silva
Patricio L. Felmer
Affiliation:
Departamento de Ing. Matemática, F.C.F.M., Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile
Elves A. de B. e Silva
Affiliation:
Departamento de Matemática, Universidade Federal de Pernambuco, Cidade Universitária, Recife, Brasil
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Synopsis

This work is devoted to the study of subharmonic solutions of a second-order Hamiltonian system

near an equilibrium point, say q = 0. The problem of existence of periodic solutions from the global point of view is also considered.

This problem has been studied for the case where the potential is positive and superquadratic. In this work a potential V that has change in sign is considered. The potential is decomposed as

where P is homogeneous, superquadratic and nondegenerate, and is of higher order near 0. In this paper the existence is shown of a sequence of subharmonic solutions of the equation above that converges to the equilibrium, such that their minimal periods converge to infinity.

This problem is approached from a variational point of view. Existence of subharmonic and periodic solutions is obtained via minimax techniques.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 5 , 1993 , pp. 819 - 834
Copyright
Copyright © Royal Society of Edinburgh 1993

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