Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 68, pp. 1-11.
Title: Limit cycles of the generalized Li\'enard differential equation
via averaging theory
Authors: Sabrina Badi (Univ. of Guelma, Algeria)
Amar Makhlouf (Univ. of Annaba, Algeria)
Abstract:
We apply the averaging theory of first and second order to a
generalized Lienard differential equation.
Our main result shows that for any $n,m \geq 1$ there are differential
equations $\ddot{x}+f(x,\dot{x})\dot{x}+ g(x)=0$, with
f and g polynomials of degree n and m respectively,
having at most $[n/2]$ and
$\max\{[(n-1)/2]+[m/2], [n+(-1)^{n+1}/2]\}$
limit cycles, where $[\cdot]$ denotes the integer part function.
Submitted August 11, 2011. Published May 02, 2012.
Math Subject Classifications: 37G15, 37C80, 37C30.
Key Words: Limit cycle; averaging theory; Lienard differential equation