Electronic Journal of Differential Equations,
Conference 05 (2000), pp. 135-171.

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

Authors: Julian Lopez-Gomez (Univ. Complutense de Madrid, Madrid, Spain)
 
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 in \cite{Ke57} and R. Osserman in
  \cite{Os57} 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 24, 2000.
Math Subject Classifications: 35K57, 35K60, 35D05.
Key Words: Metasolutions. Asymptotic behavior.