Periodic solutions of dissipative systems revisited

Periodic solutions of dissipative systems revisited

<p/> <p>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 di...

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Main Authors: G&#243;rniewicz Lech, Andres Jan
Format: Article
Language:English
Published: SpringerOpen 2006-01-01
Series:Fixed Point Theory and Applications
Online Access:http://www.fixedpointtheoryandapplications.com/content/2006/65195
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spelling doaj-37fc2b16c98e4b08b4b8245cd10b30e02020-11-24T22:57:24ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122006-01-012006165195Periodic solutions of dissipative systems revisitedG&#243;rniewicz LechAndres Jan<p/> <p>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.</p> http://www.fixedpointtheoryandapplications.com/content/2006/65195
collection DOAJ
language English
format Article
sources DOAJ
author G&#243;rniewicz Lech
Andres Jan
spellingShingle G&#243;rniewicz Lech
Andres Jan
Periodic solutions of dissipative systems revisited
Fixed Point Theory and Applications
author_facet G&#243;rniewicz Lech
Andres Jan
author_sort G&#243;rniewicz Lech
title Periodic solutions of dissipative systems revisited
title_short Periodic solutions of dissipative systems revisited
title_full Periodic solutions of dissipative systems revisited
title_fullStr Periodic solutions of dissipative systems revisited
title_full_unstemmed Periodic solutions of dissipative systems revisited
title_sort periodic solutions of dissipative systems revisited
publisher SpringerOpen
series Fixed Point Theory and Applications
issn 1687-1820
1687-1812
publishDate 2006-01-01
description <p/> <p>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.</p>
url http://www.fixedpointtheoryandapplications.com/content/2006/65195
work_keys_str_mv AT g243rniewiczlech periodicsolutionsofdissipativesystemsrevisited
AT andresjan periodicsolutionsofdissipativesystemsrevisited
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