Nonlinear Differential Equations,
Electron. J. Diff. Eqns., Conf. 05, 2000, pp. 135-171.

Large solutions, metasolutions, and asymptotic behaviour of the regular positive solutions of sublinear parabolic problems

Julian Lopez-Gomez

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

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