Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 332, Issue 1, Pages 428-440Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2006.09.007
Keywords
nonlocal evolution equation; resolvent positive operator; principal eigenvalue
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This paper is concerned with a nonlocal evolution equation which is used to model the spatial dispersal of organisms. We study the existence, uniqueness and stability of the positive steady solution for this nonlocal evolution equation under general conditions. The global dynamics are also investigated and a trichotomy of the global asymptotics is established. (c) 2006 Elsevier Inc. All rights reserved.
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