Electron. J. Diff. Eqns.,
Vol. 2005(2005), No. 143, pp. 114.
Existence of positive solutions for
nonlinear boundaryvalue problems in
unbounded domains of
Faten Toumi, Noureddine Zeddini
Abstract:
Let
be an unbounded domain in
()
with a nonempty compact boundary
.
We consider the
following nonlinear elliptic problem, in the sense of distributions,
where
are nonnegative constants with
and
is a nontrivial nonnegative
continuous function on
.
The function
is nonnegative and satisfies some appropriate conditions related
to a Kato class of functions, and
is a fixed harmonic
function in
, continuous on
.
Our aim is to prove
the existence of positive continuous solutions bounded below by a
harmonic function. For this aim we use the Schauder fixedpoint
argument and a potential theory approach.
Submitted September 30, 2005. Published December 8, 2005.
Math Subject Classifications: 34B15, 34B27.
Key Words: Green function; nonlinear elliptic equation;
positive solution; Schauder fixed point theorem.
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Faten Toumi
Département de Mathématiques
Faculté des Sciences de Tunis
Campus Universitaire, 2092 Tunis, Tunisia
email: Faten.Toumi@fsb.rnu.tn 

Noureddine Zeddini
Département de Mathématiques
Faculté des Sciences de Tunis
Campus Universitaire, 2092 Tunis, Tunisia
email: Noureddine.Zeddini@ipein.rnu.tn 
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