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.
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页数：13
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