Diaz, Jesus Ildefonso; Hernandez, Jesus Positive and free boundary solutions to singular nonlinear elliptic problems with absorption: an overview and open problems. (English) Zbl 1288.35264 Electron. J. Differ. Equ. 2014, Conf. 21, 31-44 (2014). 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. Cited in 6 Documents MSC: 35J75 Singular elliptic equations 35J61 Semilinear elliptic equations 35J92 Quasilinear elliptic equations with \(p\)-Laplacian 35B09 Positive solutions to PDEs Keywords:singular nonlinearity; positive solution; compact support solutions; free boundary problem; multiplicity; energy methods; absorption; multivalued graph PDFBibTeX XMLCite \textit{J. I. Diaz} and \textit{J. Hernandez}, Electron. J. Differ. Equ. 2014, 31--44 (2014; Zbl 1288.35264) Full Text: EMIS