Event Type:

Analysis Seminar

Date/Time:

Monday, February 25, 2019 - 12:00 to 12:50

Location:

Kidder 236

Local Speaker:

Abstract:

Fixed point methods have a wide range of applications in different disciplines of science; from economics and game theory (for instance Kakutani's fixed point theorem in the proof of min-max theorem in the context of zero-sum games) to the proof of well-posedness or at least existence of a solution for linear and nonlinear differential equations.

This talk consists of two parts: in the first part some major fixed point theorems for strict contractions and compact mappings, mostly pertaining to differential equations, will be presented. In the second part we will discuss two example applications: one is a semi-linear evolution equation for which we prove the existence and uniqueness of a mild solution, and the other is an abstract elliptic equation for which we prove the existence of a solution.