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.

中文翻译：

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一类广义Liénard平面系统的定性行为

我们研究了一类Liénard广义微分系统极限环存在/不存在的问题，其中与研究最多的情况不同，函数F不仅取决于x，而且取决于y变量。在此框架中，从案例研究开始呈现了一些新结果，而案例研究实际上已经展现出最重要的特性。特别地，所谓的“超线性情况”提出了逃逸轨道的一些新现象，将对此进行详细讨论。