Estimates on the number of limit cyclesof a generalized Abel equation

Naeem M. H. Alkoumi; Pedro J. Torres

doi:10.3934/dcds.2011.31.25

Article Contents

2011, Volume 31, Issue 1: 25-34. Doi: 10.3934/dcds.2011.31.25

This issue Previous Article Existence of solutions for a Boussinesq system on the half line and on a finite interval Next Article Non-trivial non-negative periodic solutions of a system of doubly degenerate parabolic equations with nonlocal terms

Estimates on the number of limit cycles of a generalized Abel equation

Naeem M. H. Alkoumi^1, and
Pedro J. Torres^1,

1.
Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada

Received: April 30, 2010

Revised: February 28, 2011

Published: December 2010

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Abstract

We prove new results about the number of isolated periodic solutions of a first order differential equation with a polynomial nonlinearity. Such results are applied to bound the number of limit cycles of a family of planar polynomial vector fields which generalize the so-called rigid systems.

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Mathematics Subject Classification: Primary: 34C07; Secondary: 34C25.

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