Limit cycles of the generalized polynomial Liénard differential equations

Abstract

AbstractWe apply the averaging theory of first, second and third order to the class of generalized polynomial Liénard differential equations. Our main result shows that for any n, m ≥ 1 there are differential equations of the form ẍ + f(x)ẋ + 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.