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Positive and Free Boundary Solutions to Singular Nonlinear Elliptic Problems with Absorption: An Overview and Open Problems

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Díaz Díaz, Jesús Ildefonso and Hernández, Jesús (2014) Positive and Free Boundary Solutions to Singular Nonlinear Elliptic Problems with Absorption: An Overview and Open Problems. Electronic Journal of Differential Equations. Conference (21). pp. 31-44. ISSN 1072-6691

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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.


Item Type:Article
Additional Information:

Variational and Topological Methods: Theory, Applications, Numerical Simulations, and Open Problems (2012). Electronic Journal of Differential Equations, Conference 21 (2014)

Uncontrolled Keywords:Singular nonlinearity; positive solution; compact support solutions;free boundary problem; multiplicity; energy methods; absorption; multivalued graph.
Subjects:Sciences > Mathematics > Differential equations
ID Code:29472
Deposited On:14 Apr 2015 12:34
Last Modified:12 Dec 2018 15:06

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