ANZIAM J.
46 (2004), 273-297
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Nonnegative solutions for a heterogeneous degenerate competition model
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Antonio Suárez
Dpto. Ecuaciones Diferenciales y Análisis Numérico
Fac. Matemáticas
C/ Tarfia s/n, C.P. 41012
Univ. Sevilla
Sevilla
Spain
suarez@us.es
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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.
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