Qualitative analysis of the phase portrait for a class of planar vector fields via the comparison method

Timoteo Carletti, Lilia Rosati, Gabriele Villari

Research output: Contribution to journalArticle

Abstract

The phase portrait of the second-order differential equation $$ \ddot{x} + \sum_{l=0}^n f_l(x)\dot{x}^l=0, $$ is studied. Some results concerning existence, non-existence and uniqueness of limit cycles are presented. In particular, a generalization of the classical Massera uniqueness result is proved.
Original languageEnglish
Pages (from-to)39-51
Number of pages13
JournalNonlinearAnalysis
Volume67
Publication statusPublished - 2007

Keywords

  • Qualitative theory
  • Planar vector fields
  • Limit cycles

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