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.
Submitted April 9, 2014. Published June 20, 2014.
Math Subject Classifications: 35B40, 35K57, 92D25.
Key Words: Nonlocal dispersal; upper-lower solutions; aggregation; existence and uniqueness.
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| Jian-Wen Sun |
School of Mathematics and Statistics
Lanzhou, Gansu 730000, China
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