Jesus Ildefonso Diaz, Jesus Hernandez
Abstract:
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.
Published February 10, 2014.
Math Subject Classifications: 35J75, 35J61, 35J92.
Key Words: Singular nonlinearity; positive solution; compact support solutions;
free boundary problem; multiplicity; energy methods; absorption;
multivalued graph.
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Jesús Ildefonso Díaz Instituto de Matemática Interdisciplinar Universidad Compluense de Madrid 28040 Madrid, Spain email: diaz.racefyn@insde.es | |
Jesús Hernández Departamento de Matemáticas Universidad Autónoma de Madrid 28049 Cantoblanco, Madrid, Spain email: jesus.hernandez@uam.es |
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