Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 312864, 16 pages
doi:10.1155/2010/312864
Research Article

Positive Solutions of a Singular Positone and Semipositone Boundary Value Problems for Fourth-Order Difference Equations

Chengjun Yuan1,2

1School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
2School of Mathematics and Computer, Harbin University, Harbin 150086, China

Received 13 June 2010; Revised 9 September 2010; Accepted 13 October 2010

Academic Editor: Manuel De la Sen

Copyright © 2010 Chengjun Yuan. 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

This paper studies the boundary value problems for the fourth-order nonlinear singular difference equations Δ4u(i−2)=λα(i)f(i,u(i)), i∈[2,T+2], u(0)=u(1)=0, u(T+3)=u(T+4)=0. We show the existence of positive solutions for positone and semipositone type. The nonlinear term may be singular. Two examples are also given to illustrate the main results. The arguments are based upon fixed point theorems in a cone.