ABSTRACT

This work is devoted to introduce a new Hardy-type inequality related to $p(\cdot )$-Laplacian operator. Moreover, by using the Mountain Pass theorem and the Krasnoselskii's genus theory, we show the existence and infinite solutions to the $p(\cdot )$-Kirchhoff type problem with singular nonlinearity.

中文翻译：

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关于由 p(⋅)-拉普拉斯算子驱动的奇异基尔霍夫类型问题

摘要

这项工作致力于引入一个新的 Hardy 型不等式，与$p(\cdot )$-拉普拉斯算子。此外，通过使用 Mountain Pass 定理和 Krasnoselskii 的属理论，我们证明了$p(\cdot )$-具有奇异非线性的基尔霍夫型问题。