3:30 p.m., Friday
Professor Stan Alama
Department of Mathematics and Statistics
Adventures with the mountain pass theorem: existence, multiplicity, uniqueness
Some of the most powerful tools for the study of differential
equations come from the Calculus of Variations, beginning with
Fermat's Least-action Principle and Bernoulli's solution to the
Brachistochrone problem through Dirichlet's Principle and minimal
surfaces. The celebrated Mountain-Pass Theorem of Ambrosetti and
Rabinowitz is a simple but elegant technique for finding
non-minimizing critical points, which has had enormous applicability
in ordinary and partial differential equations. While it is usually
presented as a tool for proving existence of solutions, I will give
some examples of its versatility in proving multiplicity, the
qualitative form of solutions, and even uniqueness!
Refreshments will be served in Math Annex Room 1115, 3:15 p.m.