ANZIAM  J.  46 (2004), 273-297
Nonnegative solutions for a heterogeneous degenerate competition model

Antonio Suárez
  Dpto. Ecuaciones Diferenciales y Análisis Numérico
  Fac. Matemáticas
  C/ Tarfia s/n, C.P. 41012
  Univ. Sevilla

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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