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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 314382, 9 pages
http://dx.doi.org/10.1155/2013/314382
Research Article

Some New Existence Results of Positive Solutions to an Even-Order Boundary Value Problem on Time Scales

Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, China

Received 12 April 2013; Accepted 16 May 2013

Academic Editor: Svatoslav Staněk

Copyright © 2013 Yanbin Sang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider a high-order three-point boundary value problem. Firstly, some new existence results of at least one positive solution for a noneigenvalue problem and an eigenvalue problem are established. Our approach is based on the application of three different fixed point theorems, which have extended and improved the famous Guo-Krasnosel’skii fixed point theorem at different aspects. Secondly, some examples are included to illustrate our results.