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