Theses and Dissertations

Issuing Body

Mississippi State University

Advisor

Shivaji, Ratnasingham

Committee Member

Johnson, Corlis

Committee Member

Lim, Hyeona

Committee Member

Miller, Len

Committee Member

Neumann, Michael

Other Advisors or Committee Members

Razzaghi, Mohsen

Date of Degree

8-1-2011

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

We study positive solutions to classes of steady state reaction diffusion equations that arise naturally in applications. In particular, we study models arising from population dynamics and combustion theory. The main focus of this dissertation is the mathematical analysis of a challenging new class of problems when a certain nonlinear boundary condition is satisfied. In particular, we establish existence and multiplicity results by making use of the Quadrature method, the method of sub-super solutions, and degree theory. The results in this dissertation provide a significant contribution towards the analysis of elliptic boundary value problems with nonlinear boundary conditions.

URI

https://hdl.handle.net/11668/15450

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