## Relatório de pesquisa 16/08

Limit Cycles of the Generalized Polynomial Liénard Differential Equations, Jaume Llibre, Ana Cristina Mereu and Marco Antonio Teixeira, submitted Sept. 04.

Abstract

We apply the averaging theory of first, second and third order
to the class of generalized polynomial Liénard differential
equations. Our main result shows that for any n, m greater than or
equal to 1 there are

differential equations of the form $\ddot{x}+f(x)
\dot{x}+g(x)=0$, with f and g polynomials of degree n and m
respectively, having at least [(n+m-1)/2] limit cycles, where [.]
denotes the integer part function.

Mathematics Subject Classifications
(2000): 34C29, 34C25, 47H11.

Keywords: limit cycle, periodic orbit, Liénard equation, averaging theory.

*Copy
of the file:*
rp16-08.pdf
(PDF)

rp16-08.pdf.gz (gzipped PDF)

September 04, 2008

**Volta ao
indíce de Relatórios de Pesquisa**