Title

Existence of solutions to semi-linear elliptic differential equations: Approximation and verification

Date of Completion

January 2008

Keywords

Mathematics

Degree

Ph.D.

Abstract

We investigate a conjecture regarding the number of solutions of a second order elliptic boundary value problem with an asymmetric nonlinearity. This investigation makes use of several computer assisted techniques. First we compute approximate solutions using Newton's Iteration for small b and then use a continuation method to show that the number of solutions becomes large as b increases. Lastly, we discuss how we will use interval arithmetic to show that the exact solution is indeed close to our approximate solution. ^