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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

On the existence and uniqueness of positive solutions for competing species models with diffusion


Author: E. N. Dancer
Journal: Trans. Amer. Math. Soc. 326 (1991), 829-859
MSC: Primary 35K57; Secondary 47H15, 92D25
MathSciNet review: 1028757
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Abstract: In this paper, we consider strictly positive solutions of competing species systems with diffusion under Dirichlet boundary conditions. We obtain a good understanding of when strictly positive solutions exist, obtain new nonuniqueness results and a number of other results, showing how complicated these equations can be. In particular, we consider how the shape of the underlying domain affects the behaviour of the equations.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1991-1028757-9
PII: S 0002-9947(1991)1028757-9
Keywords: Competing species systems, strictly positive solutions, uniqueness, domain perturbation
Article copyright: © Copyright 1991 American Mathematical Society