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 ẋ = y − F (x, y), ẏ = −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.