POSITIVE AND FREE BOUNDARY SOLUTIONS TO SINGULAR NONLINEAR ELLIPTIC PROBLEMS WITH ABSORPTION: AN OVERVIEW AND OPEN PROBLEMS

被引：0

作者：

Ildefonso Diaz, Jesus ^{[1
]}

Hernandez, Jesus ^{[2
]}

机构：

[1] Univ Complutense Madrid, Inst Matemat Interdisciplinar, E-28040 Madrid, Spain

[2] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2014年

关键词：

Singular nonlinearity; positive solution; compact support solutions; free boundary problem; multiplicity; energy methods; absorption; multivalued graph; EQUATIONS; REGULARITY; EXISTENCE; PRINCIPLE;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give a survey of recent results and open problems concerning existence and multiplicity of positive and/or compact support solutions to some semilinear elliptic equations with singular nonlinear terms of absorption type. This includes the case of discontinuous (at the origin) nonlinearities, which is treated by introducing maximal monotone graphs. Extensions to the p-Laplacian are also considered. The one-dimensional case is studied by using energy methods.

引用

页码：31 / 44

页数：14

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