Transactions of the American Mathematical Society

Author(s): Yihong Du; Yuan Lou
Journal: Trans. Amer. Math. Soc. 349 (1997), 2443-2475.
MSC (1991): Primary 35J55
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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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Yihong Du
Affiliation: Department of Mathematics, Statistics and Computing Science, University of New England, Armidale, NSW 2351, Australia
Email: ydu@neumann.une.edu.au

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