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...
| Authors: | , |
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| 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 |
| 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. |
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