Banach Fixed Point Theorem and Its Application to Differential Equations

Dr. Wenzhang Huang

Department of Mathematical Sciences
University of Alabama in Huntsville

November 16, 2001

Abstract

Banach fixed point theorem, one of the most import results in the nonlinear analysis, has a broad application to both pure and applied mathematics. This talk will be focused on the application of Banach point theorem to differential equations, such as the existence and uniqueness of solutions, local bifurcation, etc. In particular, we will use Banach fixed point theorem to prove the existence of an important class of solutions, the traveling wave, for the reaction-diffusion equations that have been served as the models for many problems from sciences.