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Axioms 2019, 8(1), 19; https://doi.org/10.3390/axioms8010019

Note on Limit-Periodic Solutions of the Difference Equation xt + 1 − [h(xt) + λ]xt = rt, λ > 1

1
Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech Republic
2
Centre PMF, Laboratory SAMM, Université Paris I Panthéon—Sorbonne, 90, Rue de Tolbiac, 75 634 Paris CEDEX 13, France
*
Author to whom correspondence should be addressed.
Received: 7 January 2019 / Revised: 31 January 2019 / Accepted: 1 February 2019 / Published: 5 February 2019
(This article belongs to the Special Issue New Trends in Differential and Difference Equations and Applications)
Full-Text   |   PDF [327 KB, uploaded 27 February 2019]   |   Review Reports

Abstract

As a nontrivial application of the abstract theorem developed in our recent paper titled “Limit-periodic solutions of difference and differential systems without global Lipschitzianity restricitions”, the existence of limit-periodic solutions of the difference equation from the title is proved, both in the scalar as well as vector cases. The nonlinearity h is not necessarily globally Lipschitzian. Several simple illustrative examples are supplied. View Full-Text
Keywords: limit-periodic solutions; difference equations; exponential dichotomy; strong nonlinearities; effective existence criteria; population dynamics limit-periodic solutions; difference equations; exponential dichotomy; strong nonlinearities; effective existence criteria; population dynamics
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Andres, J.; Pennequin, D. Note on Limit-Periodic Solutions of the Difference Equation xt + 1 − [h(xt) + λ]xt = rt, λ > 1. Axioms 2019, 8, 19.

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