Díaz Díaz, Jesús IldefonsoHernández, Jesús2023-06-192023-06-1920141072-6691https://hdl.handle.net/20.500.14352/33969Variational and Topological Methods: Theory, Applications, Numerical Simulations, and Open Problems (2012). Electronic Journal of Differential Equations, Conference 21 (2014)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.engjournal articlehttp://ejde.math.txstate.eduopen access517.9Singular nonlinearitypositive solutioncompact support solutionsfree boundary problemmultiplicityenergy methodsabsorptionmultivalued graph.Ecuaciones diferenciales1202.07 Ecuaciones en Diferencias