Electronic Journal of Differential Equations (Oct 2000)
Large solutions, metasolutions, and asymptotic behaviour of the regular positive solutions of sublinear parabolic problems
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.
