LIMIT CYCLES FOR GENERALIZED ABEL EQUATIONS-Reference-Cited by-同舟云学术

LIMIT CYCLES FOR GENERALIZED ABEL EQUATIONS

Published:2006-12 Issue:12 Volume:16 Page:3737-3745
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

GASULL ARMENGOL¹,GUILLAMON ANTONI²

Affiliation:

1. Dept. de Matemàtiques, Edifici Cc, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain

2. Dept. de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Dr. Marañón n.44-50, 08028, Barcelona

Abstract

This paper deals with the problem of finding upper bounds on the number of periodic solutions of a class of one-dimensional nonautonomous differential equations: those with the right-hand sides being polynomials of degree n and whose coefficients are real smooth one-periodic functions. The case n = 3 gives the so-called Abel equations which have been thoroughly studied and are well understood. We consider two natural generalizations of Abel equations. Our results extend previous works of Lins Neto and Panov and try to step forward in the understanding of the case n > 3. They can be applied, as well, to control the number of limit cycles of some planar ordinary differential equations.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127406017130

Reference21 articles.

1. Existence of Closed Solutions of an Equationẋ=f(t,x), wherefx′(t,x) is Weakly Convex or Concave inx

2. Limit cycles of a class of polynomial systems

3. R. Conti, Uniformly Isochronous Centres of Polynomial Systems in ℝ2, Lecture Notes in Pure and Applied Mathematics 152 (M. Dekker, NY, 1994) pp. 21–31.

4. Cubic Systems and Abel Equations

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