Abstract In the present paper, we consider the nonlinear periodic systems involving variable exponent driven by p(t)-Laplacian with a locally Lipschitz nonlinearity. Our arguments combine the variational principle for locally Lipschitz functions with the properties of the generalized Lebesgue-Sobolev space. Applying the non-smooth critical point theory, we establish some new existence results.

中文翻译：

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涉及 p(t)-Laplacian 的微分包含问题的周期解

摘要 在本文中，我们考虑了由具有局部 Lipschitz 非线性的 p(t)-Laplacian 驱动的涉及可变指数的非线性周期系统。我们的论点将局部 Lipschitz 函数的变分原理与广义 Lebesgue-Sobolev 空间的性质结合起来。应用非光滑临界点理论，我们建立了一些新的存在结果。