Multiplicity of periodic solutions for the planar polynomial equation (Q1590105)

Here, the authors study the existence and multiplicity of periodic solutions to the following planar polynomial equation \(\dot z = \sum_{j=0}^nc_j(t)z^j\), where \(c_j\) are periodic functions. Based on Leray-Schauder degree, they prove that this equation has at least \(s\) distinct periodic solutions if the polynomial \(\sum_{j=0}^n{\bar c_j(t)}z^j\) has \(s\) distinct roots, where \(\bar c_j(t)\) is the average of \(c_j(t)\).