Existence and uniqueness of positive solutions for a nonlocal dispersal population model

Abstract

In this article, we study the solutions of a nonlocal dispersal equation with a spatial weight representing competitions and aggregation. To overcome the limitations of comparison principles, we introduce new definitions of upper-lower solutions. The proof of existence and uniqueness of positive solutions is based on the method of monotone iteration sequences.

Keywords

• Nonlocal dispersal
• upper-lower solutions
• aggregation
• existence and uniqueness