%0 Journal Article
%T Limit cycles of the generalized Li'enard differential equation via averaging theory
%A Sabrina Badi
%A Amar Makhlouf
%J Electronic Journal of Differential Equations
%D 2012
%I Texas State University
%X 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.
%K Limit cycle
%K averaging theory
%K Lienard differential equation
%U http://ejde.math.txstate.edu/Volumes/2012/68/abstr.html