Singular boundary value problems, via Sperner's lemma

Panos K. Palamides; Alex P. Palamides

doi:10.3934/proc.2007.2007.814

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2007, Volume 2007: 814-823. Doi: 10.3934/proc.2007.2007.814 open access

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Singular boundary value problems, via Sperner's lemma

Panos K. Palamides^1, and
Alex P. Palamides^2,

1.
Naval Academy of Greece, Piraeus, 451 10
2.
University of Peloponesse, Department of Telecommunications Science and Technology, Tripolis

Received: August 31, 2006

Revised: February 28, 2007

Published: August 2007

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Abstract

Abstract

In this paper existence results of positive solutions, by means of a new approaches, for the $3^(the)$ order three-point BVP
$x'''(t) = \alpha (t) f(t, x(t), x' (t) , x'' (t)), x (0) = x' (n) = x'' (1) = 0,$
Keywords:
Three point singular boundary value problem; third order differential equation; positive solution; vector field; SpernerÃ‚Â’s lemma; fixed point; cone.

Mathematics Subject Classification: Primary 34B10, 34B18; Secondary 34B15, 34G20.

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