Mississippi State University
Other Advisors or Committee Members
Date of Degree
Dissertation - Open Access
Doctor of Philosophy
College of Arts and Sciences
Department of Mathematics and Statistics
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.
Goddard, Jerome, "Classes of reaction diffusion equations with nonlinear boundary conditions" (2011). Theses and Dissertations. 1063.