×

Positive and free boundary solutions to singular nonlinear elliptic problems with absorption: an overview and open problems. (English) Zbl 1288.35264

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.

MSC:

35J75 Singular elliptic equations
35J61 Semilinear elliptic equations
35J92 Quasilinear elliptic equations with \(p\)-Laplacian
35B09 Positive solutions to PDEs
PDFBibTeX XMLCite
Full Text: EMIS