Electron. J. Diff. Eqns.,
Vol. 2005(2005), No. 106, pp. 118.
Positive solutions of threepoint boundaryvalue problems
for pLaplacian singular differential equations
George N. Galanis, Alex P. Palamides
Abstract:
In this paper we prove the existence of positive solutions for the
threepoint singular boundaryvalue problem
subject to
or to
where
is the
Laplacian operator,
;
are fixed points and
is a monotone
continuous function defined on the real line
with
and
.
Our approach is a combination of
Nonlinear Alternative of LeraySchauder with the properties
of the associated vector field at the
plane.
More precisely, we show that the solutions of the above
boundaryvalue problem remains away from the origin for
the case where the nonlinearity is sublinear and so we avoid
its singularity at
.
Submitted May 13, 2005. Published October 7, 2005.
Math Subject Classifications: 34B15, 34B18.
Key Words: Threepoint singular boundaryvalue problem; pLaplacian;
positive and negative solutions; vector field;
Nonlinear alternative of LeraySchauder.
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George N. Galanis
Naval Academy of Greece
Piraeus, 185 39, Greece
email: ggalanis@math.uoa.gr 

Alex P. Palamides
Department of Communication Sciences
University of Peloponnese
22100 Tripolis, Greece
email: palamid@uop.gr 
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