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Positive Radial Solutions for P-Laplacian Singular Boundary Value Problems

In this dissertation, we study the existence and nonexistence of positive radial solutions for classes of quasilinear elliptic equations and systems in a ball with Dirichlet boundary conditions. Our nonlinearities are asymptotically p-linear at infinity and are allowed to be singular at zero with non-positone structure, which have not been considered in the literature. In the one parameter single equation problem, we are able to show the existence of a positive radial solution with precise lower bound estimate for a certain range of the parameter. We also extend the study to a class of asymptotically p-linear system with two parameters and in the presence of singularities. We establish the existence of a positive solution with a precise lower bound estimate when the product of the parameters is in a certain range. Necessary and sufficient conditions for the existence of a positive solution are also obtained for both the single equation and system under additional assumptions. Our approach is based on the Schauder Fixed Point Theorem.

Identiferoai:union.ndltd.org:MSSTATE/oai:scholarsjunction.msstate.edu:td-4572
Date17 August 2013
CreatorsWilliams, Jahmario
PublisherScholars Junction
Source SetsMississippi State University
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceTheses and Dissertations

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