Existence of Positive Solutions of a Discrete Elastic Beam Equation

Abstract EN

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.