Widely applicable periodicity results for higher order difference equations

István Gyori, László Horváth

Research output: Contribution to journalArticle

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, 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 proof-technique 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
JournalJournal of Difference Equations and Applications
DOIs
Publication statusAccepted/In press - 2013

Fingerprint

Higher order equation
Difference equations
Nonlinear equations
Periodicity
Difference equation
Normed Space
Recursion
Nonlinear Equations
Necessary
Sufficient Conditions
Theorem

Keywords

  • difference equation
  • generalized Lozi equation
  • global periodicity
  • linearized periodicity
  • periodic solutions
  • periodicity over a group

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Algebra and Number Theory

Cite this

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