Colloquium
3:30 p.m., Friday
Math 100
Professor Stan Alama
Department of Mathematics and Statistics
McMaster University
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 Leastaction Principle and Bernoulli's solution to the
Brachistochrone problem through Dirichlet's Principle and minimal
surfaces. The celebrated MountainPass Theorem of Ambrosetti and
Rabinowitz is a simple but elegant technique for finding
nonminimizing 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.
