Theses and Dissertations
Issuing Body
Mississippi State University
Advisor
Miller, T. Len
Committee Member
Shivaji, Ratnasingham
Committee Member
Shows, Justin H.
Committee Member
Razzaghi, Mohsen
Committee Member
Lim, Hyeona
Other Advisors or Committee Members
Johnson, Corlis P.
Date of Degree
8-15-2014
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 establish new existence, multiplicity, and uniqueness results on positive radial solutions for classes of steady state reaction diffusion equations on the exterior of a ball. In particular, for the first time in the literature, this thesis focuses on the study of solutions that satisfy a general class of nonlinear boundary conditions on the interior boundary while they approach zero at infinity (far away from the interior boundary). Such nonlinear boundary conditions occur naturally in various applications including models in the study of combustion theory. We restrict our analysis to reactions terms that grow slower than a linear function for large arguments. However, we allow all types of behavior of the reaction terms at the origin (cases when it is positive, zero, as well as negative). New results are also added to ecological systems with Dirichlet boundary conditions on the interior boundary (this is the case when the boundary is cold). We establish our existence and multiplicity results by the method of sub and super solutions and our uniqueness results via deriving a priori estimates for solutions.
URI
https://hdl.handle.net/11668/20972
Recommended Citation
Butler, Dagny Grillis, "Analysis of Classes of Nonlinear Eigenvalue Problems on Exterior Domains" (2014). Theses and Dissertations. 632.
https://scholarsjunction.msstate.edu/td/632