The multiplicity of the equatorial limit cycle of a class of planar polynomial vector fields

In this paper, we have investigated the existence and the multiplicity of the equatorial limit cycle for a class of planar vector fields of degree 2m+12m+1, obtained the necessary and sufficient condition that the equator is a closed orbit and the multiplicity of the equatorial limit cycle of the planar polynomial vector fields is m+1m+1. It is helpful to answer the second part of Hilbert’s 16th problem.