高维强奇点临界非局部问题的三种弱解

IF 2.3 3区数学 Q1 MATHEMATICS

Mathematics Pub Date : 2024-09-18 DOI:10.3390/math12182910

Gabriel Neves Cunha, Francesca Faraci, Kaye Silva

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引用次数: 0

摘要

在本文中，我们讨论了一个涉及非局部算子、临界非线性和亚临界扰动的强奇异问题。我们将非光滑分析技术应用于能量函数，并结合对其光滑部分子级拓扑特性的研究，证明了三个弱解的存在：两个局部最小点和作为山口临界点的第三个点。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Three Weak Solutions for a Critical Non-Local Problem with Strong Singularity in High Dimension

In this paper, we deal with a strongly singular problem involving a non-local operator, a critical nonlinearity, and a subcritical perturbation. We apply techniques from non-smooth analysis to the energy functional, in combination with the study of the topological properties of the sublevels of its smooth part, to prove the existence of three weak solutions: two points of local minimum and a third one as a mountain pass critical point.

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来源期刊

Mathematics Mathematics-General Mathematics

CiteScore

4.00

自引率

16.70%

发文量

4032

审稿时长

21.9 days

期刊介绍： Mathematics (ISSN 2227-7390) is an international, open access journal which provides an advanced forum for studies related to mathematical sciences. It devotes exclusively to the publication of high-quality reviews, regular research papers and short communications in all areas of pure and applied mathematics. Mathematics also publishes timely and thorough survey articles on current trends, new theoretical techniques, novel ideas and new mathematical tools in different branches of mathematics.