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Existence of positive solutions for nonlinear m-point boundary value problems on time scales

Junfang Zhao1*, Hairong Lian1 and Weigao Ge2

Author Affiliations

1 School of Science, China University of Geosciences, Beijing 100083, P.R. China

2 Department of Mathematics, Beijing Institute of Technology, Beijing 100081, P.R. China

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Boundary Value Problems 2012, 2012:4  doi:10.1186/1687-2770-2012-4

Published: 17 January 2012

Abstract

In this article, we study the following m-point boundary value problem on time scales,

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/4/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/4/mathml/M1">View MathML</a>

where <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/4/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/4/mathml/M2">View MathML</a> is a time scale such that <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/4/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/4/mathml/M3">View MathML</a>, ϕp(s) = |s|p-2s,p > 1,h Cld((0, T), (0, +∞)), and f C([0,+∞), (0,+∞)), <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/4/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/4/mathml/M4">View MathML</a>. By using several well-known fixed point theorems in a cone, the existence of at least one, two, or three positive solutions are obtained. Examples are also given in this article.

AMS Subject Classification: 34B10; 34B18; 39A10.

Keywords:
positive solutions; cone; multi-point; boundary value problem; time scale