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.

引用

页数：24

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