Open Access

Periodic solutions of dissipative systems revisited

Fixed Point Theory and Applications20062006:65195

https://doi.org/10.1155/FPTA/2006/65195

Received: 23 June 2005

Accepted: 17 October 2005

Published: 23 May 2006

Abstract

We reprove in an extremely simple way the classical theorem that time periodic dissipative systems imply the existence of harmonic periodic solutions, in the case of uniqueness. We will also show that, in the lack of uniqueness, the existence of harmonics is implied by uniform dissipativity. The localization of starting points and multiplicity of periodic solutions will be established, under suitable additional assumptions, as well. The arguments are based on the application of various asymptotic fixed point theorems of the Lefschetz and Nielsen type.

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Authors’ Affiliations

(1)
Department of Mathematics Analysis, Faculty of Science, Palacký University
(2)
Faculty of Mathematics and Informatics, Nicolaus Copernicus University

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Copyright

© J. Andres and L. Górniewicz 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.