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Zbl 1034.35062
López-Gómez, Julián
Coexistence and meta-coexistence for competing species. (English)
[J] Houston J. Math. 29, No. 2, 483-536 (2003). ISSN 0362-1588

The dynamics of a family of competing species models where one of the species grows in the presence of finitely many refuges according to a logistic law is analyzed. Obtained results show how the model behaves like a superlinear indefinite problem for a single equation. As a result of the presence of refuges, for certain ranges of values of the parameters involved in the formulation of the model, the dynamics of its classical positive solutions is regulated by a metacoexistence state. (By it is meant a solution couple consisting of a metasolution coupled with a classical regular solution.)
[Josef Dibl{\'\i}k (Brno)]

MSC 2000:: *35K50 Systems of parabolic equations, boundary value problems
35J55 Systems of elliptic equations, boundary value problems
35B32 Bifurcation (PDE)

Keywords: Competing species models; Coexistence states; Large solutions; Metasolutions; Metacoexistence states

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