On the Qualitative Behavior of a Class of Generalized Liénard Planar Systems

We study the problem of existence/nonexistence of limit cycles for a class of Liénard generalized differential systems in which, differently from the most investigated case, the function F depends not only on x but also on the y-variable. In this framework, some new results are presented, starting from a case study which, actually, already exhibits the most significant properties. In particular, the so-called “superlinear case” presents some new phenomena of escaping orbits which will be discussed in detail.