Content area
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.
Details
Title
Existence of solutions to semi-linear elliptic differential equations: Approximation and verification
Author
Termine, Lisa
Year
2008
ISBN
978-0-549-66475-8
Source type
Dissertation or Thesis
Language of publication
English
ProQuest document ID
304628147
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
