Widely applicable periodicity results for higher order difference equations

István Győri, László Horváth

Research output: Article

1 Citation (Scopus)

Abstract

In this paper we study the periodicity of higher order nonlinear equations. They are defined by a recursion which is generated by a mapping h: Xs → X, where X is a state set. Our main objective is to prove sharp conditions for the global periodicity of our equations assuming the weakest possible assumptions on the state set X. As an application of our general algebraic-like conditions we prove a new linearized global periodicity theorem assuming that X is a normed space. We needed a new prooftechnique since in the infinite dimensional case the Jacobian does not exist. We give new necessary and/or sufficient conditions as well as new examples for global periodicity, for instance whenever the state set X is a group.

Original languageEnglish
Pages (from-to)883-924
Number of pages42
JournalJournal of Difference Equations and Applications
Volume20
Issue number5
DOIs
Publication statusPublished - jan. 1 2014

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ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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