Positive and Free Boundary Solutions to Singular Nonlinear Elliptic Problems with Absorption: An Overview and Open Problems

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, whic...

Full description

Bibliographic Details
Authors: Díaz Díaz, Jesús Ildefonso, Hernández, Jesús
Format: article
Publication Date:2014
Country:España
Institution:Universidad Complutense de Madrid (UCM)
Repository:Docta Complutense
Language:English
OAI Identifier:oai:docta.ucm.es:20.500.14352/33969
Online Access:https://hdl.handle.net/20.500.14352/33969
Access Level:Open access
Keyword:517.9
Singular nonlinearity
positive solution
compact support solutions
free boundary problem
multiplicity
energy methods
absorption
multivalued graph.
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
Description
Summary: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.