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2020 Nielsen number, impulsive differential equations and problem of Jean Leray
Jan Andres
Topol. Methods Nonlinear Anal. 56(2): 383-400 (2020). DOI: 10.12775/TMNA.2019.112

Abstract

We will show that, unlike to usual (i.e. non-impulsive) differential equations, the Nielsen theory results for single-valued as well as multivalued maps on tori can be effectively applied to impulsive differential equations and inclusions. With this respect, two main aims will be focused, namely: (i) multiplicity results for harmonic periodic solutions, (ii) the coexistence of subharmonic periodic solutions with various periods. In both cases, we will try to contribute at least partly to the problem posed already in 1950 by Jean Leray. A dynamic complexity of the related maps, measured in terms of entropy, will be also examined.

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Jan Andres. "Nielsen number, impulsive differential equations and problem of Jean Leray." Topol. Methods Nonlinear Anal. 56 (2) 383 - 400, 2020. https://doi.org/10.12775/TMNA.2019.112

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Published: 2020
First available in Project Euclid: 10 September 2020

Digital Object Identifier: 10.12775/TMNA.2019.112

Rights: Copyright © 2020 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.56 • No. 2 • 2020
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