On the existence and uniqueness of limit cycles for generalized Liénard systems

In this paper, we consider a generalized Liénard systemdxdt=ϕ(y)−F(x),equation(0.1)dydt=−g(x), where F   is continuous and differentiable on an open interval (b1,a1)(b1,a1) with −∞⩽b1<00xF(x)>0 as a