Analysis of classes of superlinear semipositone problems with nonlinear boundary conditions
- UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
- Quinn A. Morris (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 for classes of steady state reaction diffusion problems on the exterior of a ball with both Dirichlet and nonlinear boundary conditions. We consider p-Laplacian problems (p>1) with reaction terms which are superlinear at infinity and semipositone. In the case p=2, using variational methods, we establish the existence of a solution, and via detailed analysis of the Green's function, we prove the positivity of the solution. In the case p[unequal to]2, we again use variational methods to establish the existence of a solution, but the positivity of the solution is achieved via sophisticated a priori estimates. In the case p[unequal to]2, the Green's function analysis is no longer available. Our results significantly enhance the literature on superlinear semipositone problems. Finally, we provide algorithms for the numerical generation of exact bifurcation curves for one-dimensional problems. In the autonomous case, we extend and analyze a quadrature method, and using nonlinear solvers in Mathematica, generate bifurcation curves. In the nonautonomous case, we employ shooting methods in Mathematica to generate bifurcation curves.
Analysis of classes of superlinear semipositone problems with nonlinear boundary conditions
PDF (Portable Document Format)
2230 KB
Created on 8/1/2017
Views: 1283
Additional Information
- Publication
- Dissertation
- Language: English
- Date: 2017
- Keywords
- Existence, P-superlinear, Quadrature method, Semipositone
- Subjects
- Nonlinear boundary value problems $x Numerical solutions
- Dirichlet problem $x Numerical solutions
- Curves $x Rectification and quadrature
- Diffusion $x Mathematical models
- Laplacian operator