Limit Cycles of a Class of Cubic Lienard Equations

In this paper, a class of polynomial Lienard systems (x) over dot = y - (a(1)x + a(2)x(2) + a(3)x(3)), (y) over dot = -(b(1)x + b(2)x(2) + b(3)x(3)), is considered. Some conditions of the existence, non-existence and uniqueness of limit cycles are obtained by using Filippov transformations and Zhang's theorem. We obtain that the above system has at most one limit cycle surrounding the origin if a(1)a(3) < 0 or b(2) = 0. And, one example is given to illustrate that the system can have three limit cycles.