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Periodic solutions of dissipative systems revisited

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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Correspondence to Jan Andres.

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Andres, J., Górniewicz, L. Periodic solutions of dissipative systems revisited. Fixed Point Theory Appl 2006, 65195 (2006). https://doi.org/10.1155/FPTA/2006/65195

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Keywords

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