Periodic solutions of linear, Riccati, and Abel dynamic equations

Martin Bohner, Armengol Gasull, Claudia Valls

Research output: Contribution to journalArticleResearch

2 Citations (Scopus)

Abstract

© 2018 Elsevier Inc. We study the number of periodic solutions of linear, Riccati and Abel dynamic equations in the time scales setting. In this way, we recover known results for corresponding differential equations and obtain new results for associated difference equations. In particular, we prove that there is no upper bound for the number of isolated periodic solutions of Abel difference equations. One of the main tools introduced to get our results is a suitable Melnikov function. This is the first time that Melnikov functions are used for dynamic equations on time scales.
Original languageEnglish
Pages (from-to)733-749
JournalJournal of Mathematical Analysis and Applications
Volume470
DOIs
Publication statusPublished - 15 Feb 2019

Keywords

  • Linear, Riccati and Abel differential and difference equations
  • Melnikov function
  • Periodic function
  • Time scales

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