Existence and uniqueness of limit cycles for generalized phi-Laplacian Lienard equations

Abstract

The Lienard equation x + f (x)x' + g(x) = 0 appears as a model in many problems of science and engineering. Since the first half of the 20th century, many papers have appeared providing existence and uniqueness conditions for limit cycles of Lienard equations. In this paper we extend some of these results for the case of the generalized phi-Laplacian Lienard equation, (phi(x'))' f(x)psi(x') + g(x) = 0. This generalization appears when derivations of the equation different from the classical one are considered. In particular, the relativistic van der Pol equation, (x'/root 1 - (x'/c)(2))' + mu(x(2) - 1)x' + x = 0, has a unique periodic orbit when mu = 0. (C) 2016 Elsevier Inc. All rights reserved.