Abstract
In studying bifurcation of Hamiltonian system with small perturbation, it can not always be obtained the uniqueness of limit cycle uniformly for0 < e ≪ 1 from monotonicity of I2(h)/I1(h), in case the first order Melnikov function M1(h)=μI1(h) + vI2(h) is degenerate at the end points of the interval of its definition. In this paper two examples have been constructed for showing the above conclusion.
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