关于具有超临界增长的 $p(x)$ 拉普拉斯方程的一些多重解

arXiv - MATH - Functional Analysis Pub Date : 2024-09-17 DOI:arxiv-2409.10984

Lin Zhao

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引用次数: 0

摘要

我们通过里切利原理考虑了涉及超临界索波列夫增长的 $p(x)$ 拉普拉奇问题解的多重性。通过截断与 De Giorgi 迭代相结合的方法，我们可以将亚临界和临界增长的结果扩展到超临界增长，并得到 $p(x)$ 拉普拉斯问题的至少三个解。

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On some multiple solutions for a $p(x)$-Laplace equation with supercritical growth

We consider the multiplicity of solutions for the $p(x)$-Laplacian problems involving the supercritical Sobolev growth via Ricceri's principle. By means of the truncation combining with De Giorgi iteration, we can extend the result about subcritical and critical growth to the supercritical growth and obtain at least three solutions for the $p(x)$ Laplacian problem.

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arXiv - MATH - Functional Analysis

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