Limit cycles in discontinuous classical Lienard equations

We study the number of limit cycles which can bifurcate from the periodic orbits of a linear center perturbed by nonlinear functions inside the class of all classical polynomial Lienard differential equations allowing discontinuities. In particular our results show that for any n >= 1 there are differential equations of the form (x) over dot+f (x)(x) over dot + x+sgn( (x) over dot)g(x) = 0, with f and g polynomials of degree n and 1 respectively, having [n/2] 1 limit cycles, where [.] denotes the integer part function. (C) 2014 Elsevier Ltd. All rights reserved.