Existence of solutions to semi-linear elliptic differential equations: Approximation and verification
Date of Completion
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. ^
Termine, Lisa, "Existence of solutions to semi-linear elliptic differential equations: Approximation and verification" (2008). Doctoral Dissertations. AAI3317857.