We 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. © 2009 Cambridge Philosophical Society.
|Journal||Mathematical Proceedings of the Cambridge Philosophical Society|
|Publication status||Published - 1 Mar 2010|