Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 582919, 15 pages
Research Article

Existence of Positive Solutions of a Discrete Elastic Beam Equation

Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Received 14 November 2009; Accepted 26 February 2010

Academic Editor: Josef Diblik

Copyright © 2010 Ruyun Ma 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.


Let T be an integer with T5 and let T2={2,3,,T}. We consider the existence of positive solutions of the nonlinear boundary value problems of fourth-order difference equations Δ4u(t2)ra(t)f(u(t))=0, tT2, u(1)=u(T+1)=Δ2u(0)=Δ2u(T)=0, where r is a constant, a:T2(0,),  and  f:[0,)[0,) is continuous. Our approaches are based on the Krein-Rutman theorem and the global bifurcation theorem.