The goal of this paper is to study the number of limit cycles that can
bifurcate from the periodic orbits of a linear center perturbed by
nonlinear functions inside the class of all generalized Liénard
di¤erential equations allowing discontinuities. In particular our
results show that for any n 1 there are di¤erential equations of the
form x¨+f(x; x_ )x_ +x+sgn(x_ )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.