Continuing the investigation for the number of crossing limit cycles of nonsmooth Li\'enard systems in [Nonlinearity 21(2008), 2121-2142] for the case of a unique equilibrium, in this paper we consider the case of any number of equilibria. We give results about the existence and uniqueness of crossing limit cycles, which hold not only for a unique equilibrium but also for multiple equilibria. Moreover, we find a sufficient condition for the nonexistence of crossing limit cycles. Finally, applying our results we prove the uniqueness of crossing limit cycles for planar piecewise linear systems with a line of discontinuity and without sliding sets.

中文翻译：

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非光滑 Liénard 系统的穿越周期轨道及其应用

继续研究 [Nonlinearity 21(2008), 2121-2142] 中非光滑 Li\'enard 系统的交叉极限环数的唯一平衡情况，在本文中，我们考虑任意数量的平衡情况。我们给出了关于交叉极限环的存在性和唯一性的结果，它不仅适用于唯一均衡，而且适用于多重均衡。此外，我们找到了不存在交叉极限环的充分条件。最后，应用我们的结果，我们证明了具有不连续线且没有滑动集的平面分段线性系统跨越极限环的唯一性。