Electron. J. Diff. Equ., Vol. 2012 (2012), No. 68, pp. 1-11.

Limit cycles of the generalized Lienard differential equation via averaging theory

Sabrina Badi, Amar Makhlouf

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 2, 2012.
Math Subject Classifications: 37G15, 37C80, 37C30.
Key Words: Limit cycle; averaging theory; Lienard differential equation

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Sabrina Badi
Department of Mathematics, University of Guelma
P.O. Box 401, Guelma 24000, Algeria
email: badisabrina@yahoo.fr
Amar Makhlouf
Department of Mathematics, University of Annaba
P.O. Box 12, Annaba 23000, Algeria
email: makhloufamar@yahoo.fr

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