Alex P. Palamides, Anastasia N. Veloni
We find a Green's function for the singular third-order three-point BVP
where . Then we apply the classical Krasnosel'skii's fixed point theorem for finding solutions in a cone. Although this problem Green's function is not positive, the obtained solution is still positive and increasing. Our techniques rely on a combination of a fixed point theorem and the properties of the corresponding vector field.
Submitted October 11, 2007. Published November 13, 2007.
Math Subject Classifications: 34B15, 34B18, 34B10, 34B16.
Key Words: Three-point singular boundary-value problem; fixed point in cones; third-order differential equation; positive solution; Green's function; vector field.
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| Alex P. Palamides |
Department of Telecommunications Science and Technology
University of Peloponnese
Karaiskaki Str., 22100 Tripolis, Greece
| Anastasia N. Veloni |
Technological Education Institute of Piraeus
Department of Electronic Computer Systems
P. Ralli Ave. & Thivon Ave. 250
Aigaleo 12244, Athens, Greece
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