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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 578672, 10 pages
http://dx.doi.org/10.1155/2014/578672
Research Article

The Existence of Positive Solutions for a Fourth-Order Difference Equation with Sum Form Boundary Conditions

1School of Electrical Engineering, Hebei University of Science and Technology, Shijiazhuang, Hebei 050018, China
2College of Sciences, Hebei University of Science and Technology, Shijiazhuang, Hebei 050018, China

Received 10 March 2014; Accepted 13 May 2014; Published 17 July 2014

Academic Editor: Abdul Latif

Copyright © 2014 Yanping Guo et al. 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 the fourth-order difference equation: ,   subject to the boundary conditions: , , , where and for ,   is continuous. is nonnegative ; is nonnegative for . Using fixed point theorem of cone expansion and compression of norm type and Hölder’s inequality, various existence, multiplicity, and nonexistence results of positive solutions for above problem are derived, which extends and improves some known recent results.