Theses and Dissertations
Issuing Body
Mississippi State University
Advisor
Shivaji, Ratnasingham
Committee Member
Neumann, Michael M.
Committee Member
Miller, Len
Committee Member
Lim, Hyeona
Committee Member
Yarahmadian, Shantia
Date of Degree
8-11-2012
Document Type
Dissertation - Open Access
Major
Mathematical Sciences
Degree Name
Doctor of Philosophy
College
College of Arts and Sciences
Department
Department of Mathematics and Statistics
Abstract
In this dissertation we study positive solutions to a singular p-Laplacian elliptic boundary value problem on a bounded domain with smooth boundary when a positive parameter varies. Our main focus is the analysis of a challenging class of singular p-Laplacian problems. We establish the existence of a positive solution for all positive values of the parameter and the existence of at least two positive solutions for a certain explicit range of the parameter. In the Laplacian case, we also prove the uniqueness of the positive solution for large values of the parameter. We extend our existence and multiplicity results to classes of singular systems and to the case when a domain is an exterior domain. We prove our existence and multiplicity results by the method of sub and supersolutions and our uniqueness result by establishing apriori and boundary estimates. Such results are well known in the literature for the nonsingular case. In this study, we extend these results to the more difficult singular case.
URI
https://hdl.handle.net/11668/20179
Recommended Citation
Ko, Eunkyung, "Analysis of Classes of Singular Boundary Value Problems" (2012). Theses and Dissertations. 633.
https://scholarsjunction.msstate.edu/td/633