On the Existence and Uniqueness of Positive Solution for a Degenerate Reaction-Diffusion Problem

Abstract

The objective of this paper is to show the existence and uniqueness of positive solutions for a class of quasilinear degenerate parabolic reaction-diffusion problems defined in a bounded domain, which have many applications in various applied sciences. Its specificity lies in the introduction of degenerate diffusion. Our approach towards our goal is mainly based on the method of upper and lower solutions. The result obtained is applied to the Lotka-Volterra model.