LIMIT CYCLES OF THE GENERALIZED LIÉNARD DIFFERENTIAL EQUATION VIA AVERAGING THEORY.

We apply the averaging theory of first and second order to a generalized Liénard differential equation. Our main result shows that for any n, m ≥ 1 there are differential equations Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed., with f and g polynomials of degree n and m respectively, having at most [n/2] and n+1 max{[(n - 1)/2] + [m/2], [n + (-1)n+1/2]} limit cycles, where [·] denotes the integer part function. [ABSTRACT FROM AUTHOR]