LIMIT CYCLE BIFURCATIONS IN A CLASS OF PIECEWISE SMOOTH DIFFERENTIAL SYSTEMS UNDER NON-SMOOTH PERTURBATIONS

This paper deals with the problem of limit cycles of a class of piecewise smooth integrable differential systems with switching line $ x = 0 $. The generating functions of the associated first order Melnikov function satisfy two different Picard-Fuchs equations. By using the property of Chebyshev space, we obtain an upper bound for the number of limit cycles bifurcating from the period annulus under non-smooth perturbations of polynomials of degree $ n $. Finally, we present a concrete example to illustrate the theoretical result.