In this paper we study implicit obstacle problems driven by a nonhomogenous differential operator, called double phase operator, and a multivalued term which is described by Clarke’s generalized gradient. Based on a surjectivity theorem for multivalued mappings, Kluge’s fixed point principle and tools from nonsmooth analysis, we prove the existence of at least one solution.

中文翻译：

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涉及多值算子的双相隐式障碍问题的存在性结果

在本文中，我们研究了由非均质微分算子（称为双相算子）和由克拉克广义梯度描述的多值项驱动的隐式障碍问题。基于多值映射的外射定理，非光滑分析的Kluge定点原理和工具，我们证明了至少一个解的存在。