Theses and Dissertations

Issuing Body

Mississippi State University

Advisor

Neumann, Michael M.

Committee Member

Razzaghi, Mohsen

Committee Member

Shivaji, Ratnasingham

Committee Member

Yarahmadian, Shantia

Committee Member

Miller, T. Len

Date of Degree

8-17-2013

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

The investigation of positive steady states to reaction diffusion models in bounded domains with Dirichlet boundary conditions has been of great interest since the 1960’s. We study reaction diffusion models where the reaction term is negative at the origin. In the literature, such problems are referred to as semipositone problems and have been studied for the last 30 years. In this dissertation, we extend the theory of semipositone problems to classes of singular semipositone problems where the reaction term has singularities at certain locations in the domain. In particular, we consider problems where the reaction term approaches negative infinity at these locations. We establish several existence results when the domain is a smooth bounded region or an exterior domain. Some uniqueness results are also obtained. Our existence results are achieved by the method of sub and super solutions, while our uniqueness results are proved by establishing a priori estimates and analyzing structural properties of the solution. We also extend many of our results to systems.

URI

https://hdl.handle.net/11668/20763

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