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Some uniqueness and exact multiplicity results for a predator-prey model


Authors: Yihong Du and Yuan Lou
Journal: Trans. Amer. Math. Soc. 349 (1997), 2443-2475
MSC (1991): Primary 35J55
DOI: https://doi.org/10.1090/S0002-9947-97-01842-4
MathSciNet review: 1401768
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Abstract: In this paper, we consider positive solutions of a predator-prey model with diffusion and under homogeneous Dirichlet boundary conditions. It turns out that a certain parameter $m$ in this model plays a very important role. A good understanding of the existence, stability and number of positive solutions is gained when $m$ is large. In particular, we obtain various results on the exact number of positive solutions. Our results for large $m$ reveal interesting contrast with that for the well-studied case $m=0$, i.e., the classical Lotka-Volterra predator-prey model.


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Additional Information

Yihong Du
Affiliation: Department of Mathematics, Statistics and Computing Science, University of New England, Armidale, NSW 2351, Australia
Email: ydu@neumann.une.edu.au

Yuan Lou
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Address at time of publication: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Email: lou@math.uchicago.edu

DOI: https://doi.org/10.1090/S0002-9947-97-01842-4
Received by editor(s): March 13, 1995
Received by editor(s) in revised form: December 4, 1995
Article copyright: © Copyright 1997 American Mathematical Society

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