Nontrivial limit cycles in a kind of piecewise smooth generalized Abel equation

In this talk, we focus on the number of nontrivial limit cycles in a kind of piecewise smooth generalized Abel equation. By employing Melnikov functions of any order and using properties of Chebyshev systems, we proved that if the degree of the Able equation is odd, then the maximum number of nontrivial limit cycles bifurcating from the periodic annulus of the unperturbed system is 6 and it can be attained, and if the degree is even, then the maximum number is 3, and it can be attained.