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.

Abstract

Let T∈ℕ 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(t−1)+λa(t)f(u(t))=0, t∈𝕋, u(0)=u(T+1)=0, where a:𝕋→ℝ+, f∈C([0,∞),[0,∞)) and, f(s)>0 for s>0, and f0=f∞=0, f0=lim⁡s→0+f(s)/s, f∞=lim⁡s→+∞f(s)/s. We investigate the global structure of positive solutions by using the Rabinowitz's global bifurcation theorem.