Limit cycles for some abel equations having coefficients without fixed signs

J. L. Bravo, M. FernÁndez, A. Gasull

Research output: Contribution to journalArticleResearchpeer-review

21 Citations (Scopus)

Abstract

We prove that some 2π-periodic generalized Abel equations of the form x′ = A(t)xn + B(t)xm + C(t)x, with n ≠ m and n, m < 2 have at most three limit cycles. The novelty of our result is that, in contrast with other results of the literature, our hypotheses allow the functions A,B, and C to change sign. Finally we study in more detail the Abel equation x′ = A(t)x3 + B(t)x2, where the functions A and B are trigonometric polynomials of degree one. © 2009 World Scientific Publishing Company.
Original languageEnglish
Pages (from-to)3869-3876
JournalInternational Journal of Bifurcation and Chaos
Volume19
Issue number11
DOIs
Publication statusPublished - 1 Jan 2009

Keywords

  • Abel equation
  • Limit cycle
  • Periodic solution

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