Abstract
In this paper, we focus on the number of nontrivial limit cycles in a kind of piecewise smooth generalized Abel equation [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. Under the condition [Formula: see text], employing Melnikov functions of any order and using properties of Chebyshev systems, we prove that if [Formula: see text] is odd, then the maximum number of nontrivial limit cycles bifurcating from the periodic annulus of the unperturbed system is 6 and it is attainable, and if [Formula: see text] is even, then the maximum number is 3, and it can be attained too.
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