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

被引：0

作者：

Cunha, Gabriel Neves ^{[1
]}

Faraci, Francesca ^{[2
]}

Silva, Kaye ^{[1
]}

机构：

[1] Univ Fed Goias, Inst Matemat & Estat, BR-74001970 Goiania, Brazil

[2] Univ Catania, Dept Math & Comp Sci, I-95125 Catania, Italy

来源：

MATHEMATICS | 2024年 / 12卷 / 18期

关键词：

strong singularity; critical nonlinearity; non-local operator; subcritical perturbation; topology of sublevels; Szulkin functional; POSITIVE SOLUTIONS; EXISTENCE; EQUATIONS;

D O I：

10.3390/math12182910

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：13

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