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Nonnegative solutions for a heterogeneous degenerate competition model

Published online by Cambridge University Press:  17 February 2009

Antonio Suárez
Antonio Suárez
Affiliation:
Dpto. Ecuaciones Diferenciales y Análisis Numérico, Fac. Matemáticas, C/ Tarfia s/n, C.P. 41012, Univ. Sevilla, Sevilla, Spain; e-mail: [email protected].
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Abstract

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This paper deals with the existence, uniqueness and qualitative properties of nonnegative and nontrivial solutions of a spatially heterogeneous Lotka-Volterra competition model with nonlinear diffusion. We give conditions in terms of the coefficients involved in the setting of the problem which assure the existence of nonnegative solutions as well as the uniqueness of a positive solution. In order to obtain these results we employ monotonicity methods, singular spectral theory and a fixed point index.

Type
Research Article
Information
The ANZIAM Journal , Volume 46 , Issue 2 , October 2004 , pp. 273 - 297
Copyright
Copyright © Australian Mathematical Society 2004

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