We are concerned with the existence of periodic solutions for potential differential inclusions involving the p-relativistic operator

$$\begin{aligned} {\mathcal {R}}_pu:= \left( \frac{|u'|^{p-2}u'}{(1-|u'|^p)^{1-1/p}} \right) ' \end{aligned}$$

and an (possible) unbounded discontinuous gradient. The approach relies on critical point theory for locally Lipschitz perturbations of convex, lower semicontinuous functions. The solutions we obtain appear as either minimizers or saddle points of the corresponding energy functional. Some examples of applications illustrating the general results are provided.

中文翻译：

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具有p-相对论算子和无穷间断非线性系统的周期解。

我们担心涉及p-相对论算子的潜在微分包含的周期解的存在

$$ \ begin {aligned} {\ mathcal {R}} _ pu：= \ left（\ frac {| u'| ^ {p-2} u'} {（1- | u'| ^ p）^ {1 -1 / p}} \ right）'\ end {aligned} $$

和（可能）无界的不连续渐变。该方法依赖于临界点理论来处理凸，下半连续函数的局部Lipschitz扰动。我们获得的解决方案显示为相应能量函数的最小化点或鞍点。提供了一些说明一般结果的应用示例。