Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 582919, 15 pages
doi:10.1155/2010/582919

Existence of positive solutions of a discrete elastic beam equation

Abstract

Let T be an integer with T≥5 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(t−2)−ra(t)f(u(t))=0, t∈T2, 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.