Limit Cycles Generated by Perturbing a Kind of Quadratic Reversible Center of a Piecewise Polynomial Differential System

In this paper, we study the number of limit cycles [Formula: see text] of the quadratic reversible system (r19) with the switching curve [Formula: see text] under the perturbations of piecewise polynomials of [Formula: see text] with degree n. By using the first-order Melnikov function, it is proved that [Formula: see text] for [Formula: see text], [Formula: see text] for [Formula: see text], and [Formula: see text] for [Formula: see text]. It is also proved that the exact cyclicity of system (r19) under the smooth perturbations of polynomials of [Formula: see text] with degree n is n by the first-order Melnikov function. The results in this paper improve the estimations about the limit cycles bifurcating from (r19) in the literature.