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Periodic solutions of dissipative systems revisited
Fixed Point Theory and Applications volume 2006, Article number: 65195 (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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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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DOI: https://doi.org/10.1155/FPTA/2006/65195