The topological degree is a tool we use to prove the existence of solutions to an equation. There are so many applications for this method. In this talk, I will focus on the introduction to the paper [1], which was done by R.A.GARDNER (1982). This presentation contains 4 parts. First, I will introduce the 2-species competition model and the problem of the existence of a traveling wave solution. Next, I’ll briefly present the primary tool, the Topological Degree Theory. Finally, I’ll apply the degree theory to the model to prove the existence of a traveling wave solution. The stability of the traveling wave solution will be discussed if time allows.

 

Reference

[1]: Robert A.Gardner.Existence and stability of travelling wave solutions of competition models: A degree theoretic approach. J.Differential Equations,44(3):343–364,1982.