Existence results for the 1-Laplacian problem with a critical concave-convex nonlinearity

被引：0
作者：
Pimenta, Marcos T. O. [1 ]
Carranza, Yino B. C. [2 ]
Figueiredo, Giovany M. [3 ]
机构：
[1] Univ Estadual Paulista Unesp, Dept Matemat & Comp, BR-19060900 Presidente Prudente, SP, Brazil
[2] UNESP, Inst Biociencias Letras & Ciencias Exatas IBILCE, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil
[3] Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF, Brazil
来源：
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS | 2024年 / 26卷 / 04期
关键词：
1-Laplacian operator; singular nonlinearity; critical growth; MULTIPLE POSITIVE SOLUTIONS; LINEAR ELLIPTIC-EQUATIONS; DIRICHLET PROBLEM; SOBOLEV;
D O I：
10.1007/s11784-024-01138-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study a critical concave-convex type problem involving the 1-Laplacian operator in a general Lipschitz-continuous domain. We show an existence result using an approximation method, in which the solution is obtained as limit of solutions to p-Laplacian type problems. To overcome the lack of compactness, a version of the well-known Concentration Compactness Principle of Lions is used.
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页数：24
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