TITLE

# EXISTENCE OF POSITIVE SOLUTIONS FOR NONLINEAR BOUNDARY VALUE PROBLEMS IN BOUNDED DOMAINS OF Rn

AUTHOR(S)
Toumi, Faten
PUB. DATE
January 2006
SOURCE
Abstract & Applied Analysis;2006, p1
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
Let D be a bounded domain in â„n (n â‰¥ 2). We consider the following nonlinear elliptic problem: Î”u = f (Â·,u) in D (in the sense of distributions), uâˆ£âˆ‚D = Ï†, where Ï† is a nonnegative continuous function on âˆ‚D and f is a nonnegative function satisfying some appropriate conditions related to some Kato class of functions K(D). Our aim is to prove that the above problem has a continuous positive solution bounded below by a fixed harmonic function, which is continuous on DÂ¯. Next, we will be interested in the Dirichlet problem Î”u= -Ï(Â·,u) in D (in the sense of distributions), uâˆ£âˆ‚D = 0, where ? is a nonnegative function satisfying some assumptions detailed below. Our approach is based on the Schauder fixed-point theorem.
ACCESSION #
24049420

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