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  • Research Article
  • Open Access

Periodic solutions of dissipative systems revisited

Fixed Point Theory and Applications20062006:65195

  • Received: 23 June 2005
  • Accepted: 17 October 2005
  • Published:


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.


  • Periodic Solution
  • Point Theorem
  • Differential Geometry
  • Additional Assumption
  • Fixed Point Theorem


Authors’ Affiliations

Department of Mathematics Analysis, Faculty of Science, Palacký University, Tomkova 40, Olomouc-Hejčín, 779 00, Czech Republic
Faculty of Mathematics and Informatics, Nicolaus Copernicus University, Chopina 12/18, Torun, 87-100, Poland


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© J. Andres and L. Górniewicz 2006

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