A Chebyshev criterion with applications

A. Gasull, A. Geyer, F. Mañosas

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

We show that a family of certain definite integrals forms a Chebyshev system if two families of associated functions appearing in their integrands are Chebyshev systems as well. We apply this criterion to several examples which appear in the context of perturbations of periodic non-autonomous ODEs to determine bounds on the number of isolated periodic solutions, as well as to persistence problems of periodic solutions for perturbed Hamiltonian systems.

Original languageEnglish
Pages (from-to)6641-6655
Number of pages15
JournalJournal of Differential Equations
Volume269
Issue number9
DOIs
Publication statusPublished - 2020

Keywords

  • Abelian integral
  • Bifurcation of limit cycles
  • Chebyshev system
  • Melnikov function

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