Existence and Multiplicity of Positive Solutions of a Nonlinear Discrete Fourth‐Order Boundary Value Problem

Abstract

we show the existence and multiplicity of positive solutions of the nonlinear discrete fourth‐order boundary value problem Δ4u(t − 2) = λh(t)f(u(t)), t ∈ 𝕋2, u(1) = u(T + 1) = Δ2u(0) = Δ2u(T) = 0, where λ > 0, h : 𝕋2 → (0, ∞) is continuous, and f : ℝ → [0, ∞) is continuous, T > 4, 𝕋2 = {2,3, …, T}. The main tool is the Dancer′s global bifurcation theorem.