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Existence of positive solutions of a discrete elastic beam equation. (English) Zbl 1188.39008

Let T be an integer with T5 and let 𝕋 2 ={2,3,,T}. We consider the existence of positive solutions of the nonlinear boundary value problems of fourth-order difference equations

Δ 4 u(t-2)-ra(t)f(u(t))=0,t𝕋 2 ,u(1)=u(T+1)=Δ 2 u(0)=Δ 2 u(T)=0,

where r is a constant, a:𝕋 2 (0,), and f:[0,)[0,) is continuous. Our approaches are based on the Krein-Rutman theorem and the global bifurcation theorem.

MSC:
39A12Discrete version of topics in analysis
34B15Nonlinear boundary value problems for ODE
74K10Rods (beams, columns, shafts, arches, rings, etc.) in solid mechanics
39A10Additive difference equations