Departamento de Matematica Aplicada
Universidad Complutense de Madrid
28040-MADRID, Spain.
Phone (34) 91-394-4194, Fax (34) 91-394-4102
e-mail: Lopez_Gomez@mat.ucm.es
Julian Lopez-Gomez
Abstract:
In this paper we analyze the existence of regular and large
positive solutions for a class of non-linear elliptic boundary
value problems of logistic type in the presence of refuges. These
solutions describe the asymptotic behaviour of the regular
positive solutions of the associated parabolic model. The main
tool in our analysis is an extension of the interior estimates
found by J. B. Keller and R. Osserman
to cover the case of changing sign nonlinearities
combined with the construction of adequate sub and supersolutions.
The supersolutions are far from obvious since the nonlinearity
vanishes in finitely many regions of the underlying support
domain.
Published October 25, 2000.
Math Subject Classifications: 35K57, 35K60, 35D05.
Key Words: Large solutions. Metasolutions. Asymptotic behavior.
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Julian Lopez-Gomez Departamento de Matematica Aplicada Universidad Complutense de Madrid 28040-MADRID, Spain. Phone (34) 91-394-4194, Fax (34) 91-394-4102 e-mail: Lopez_Gomez@mat.ucm.es |
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