A class of planar differential systems with explicit expression for two limit cycles

The existence of limit cycles is interesting and very important in applications. It is a key to understand the dynamic of polynomial differential systems. The aim of this paper is to investigate a class of a multi-parameter planar polynomial differential systems. Under some suitable conditions, the existence of two limit cycles, these limit cycles are explicitly given. Some examples are presented in order to illustrate the applicability of our results. algebras.