Analysis of classes of singular steady state reaction diffusion equations
- UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
- Byungjae Son (Creator)
- Institution
- The University of North Carolina at Greensboro (UNCG )
- Web Site: http://library.uncg.edu/
- Advisor
- Ratnasingham Shivaji
Abstract: We study positive radial solutions to classes of steady state reaction diffusion problems on the exterior of a ball with both Dirichlet and nonlinear boundary conditions. We study both Laplacian as well as p-Laplacian problems with reaction terms that are p-sublinear at infinity. We consider both positone and semipositone reaction terms and establish existence, multiplicity and uniqueness results. Our existence and multiplicity results are achieved by a method of sub-supersolutions and uniqueness results via a combination of maximum principles, comparison principles, energy arguments and a-priori estimates. Our results significantly enhance the literature on p-sublinear positone and semipositone problems. Finally, we provide exact bifurcation curves for several one-dimensional problems. In the autonomous case, we extend and analyze a quadrature method, and in the nonautonomous case, we employ shooting methods. We use numerical solvers in Mathematica to generate the bifurcation curves.
Analysis of classes of singular steady state reaction diffusion equations
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Created on 8/1/2017
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Additional Information
- Publication
- Dissertation
- Language: English
- Date: 2017
- Keywords
- Dirichlet boundary conditions, Exterior of a ball, Nonlinear boundary conditions, Positive radial solutions, Steady state reaction diffusion equations
- Subjects
- Reaction-diffusion equations $x Numerical solutions
- Boundary value problems $x Numerical solutions
- Dirichlet problem $x Numerical solutions
- Bifurcation theory