Advances in Difference Equations
Volume 2009 (2009), Article ID 671625, 15 pages
Research Article

A Global Description of the Positive Solutions of Sublinear Second-Order Discrete Boundary Value Problems

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

Received 12 February 2009; Accepted 20 August 2009

Academic Editor: Svatoslav Staněk

Copyright © 2009 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 T>1, 𝕋:={1,,T}, 𝕋^:={0,1,,T+1}. We consider boundary value problems of nonlinear second-order difference equations of the form Δ2u(t1)+λa(t)f(u(t))=0, t𝕋, u(0)=u(T+1)=0, where a:𝕋+, fC([0,),[0,)) and, f(s)>0 for s>0, and f0=f=0, f0=lims0+f(s)/s, f=lims+f(s)/s. We investigate the global structure of positive solutions by using the Rabinowitz's global bifurcation theorem.