Limit cycles of the generalized polynomial Li′enard differential equations

摘要

We apply the averaging theory of first, second and third order to the class of generalized polynomial Li′enard differential equations. Our main result shows that for any n,m 1 there are differential equations of the formx + f (x) x + g(x) = 0, with f and g polynomials of degree n and m respectively, having at least [(n + m 1)/2] limit cycles, where [] denotes the integer part function.