The Exact Bound of the Number of Limit Cycles Bifurcating from the Global Nilpotent Center with a Nonlinear Switching Curve

Abstract

In this paper, we study the bifurcations of a class of planar Hamiltonian systems having a global nilpotent center under the perturbations of polynomials of degree [Formula: see text] with a nonlinear switching curve. We obtain the exact bound of the number of limit cycles bifurcating from the period annulus if the first order Melnikov function is not identically zero. We also give some examples to illustrate our results.