Remarks on a class of generalized Lienard planar systems

We continue the recent investigation [40] about the qualitative properties of the solutions for a class of generalized Lienard 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(·, y). The case of asymmetric conditions at infinity for g(x) and F(x, ·) 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.