George N. Galanis, Alex P. Palamides
In this paper we prove the existence of positive solutions for the three-point singular boundary-value problem
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 Leray-Schauder with the properties of the associated vector field at the plane. More precisely, we show that the solutions of the above boundary-value 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: Three-point singular boundary-value problem; p-Laplacian; positive and negative solutions; vector field; Nonlinear alternative of Leray-Schauder.
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| George N. Galanis |
Naval Academy of Greece
Piraeus, 185 39, Greece
| Alex P. Palamides |
Department of Communication Sciences
University of Peloponnese
22100 Tripolis, Greece
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