Remarks on a class of generalized Liénard planar systems

We continue the recent investigation [40] about the qualitative properties of the solutions for a class of generalized Liénard systems of the form x' = y - F(x; y); y'= -g(x): We present some results on the existence/non-existence of limit cycles depending on different growth assumptions of F(x, y): The case of asymmetric conditions at infinity for g(x) and F(x,y) is also examined. In the second part of the article we consider also a bifurcation result for small limit cycles as well as we discuss the complex dynamics associated to a periodically perturbed reversible system.