Existence and Multiplicity of Positive Solutions of a Nonlinear Discrete Fourth-Order Boundary Value Problem. (12th March 2012) - Ma, Ruyun; Lu, Yanqiong
Abstract : we show the existence and multiplicity of positive solutions of the nonlinear discrete fourth-order boundary value problem Δ 4 u t - 2 = λ h t f u t, t ∈ T 2, u 1 = u T + 1 = Δ 2 u 0 = Δ 2 u T = 0, where λ > 0, h : T 2 → ( 0, ∞ ) is continuous, and f : R → [ 0, ∞ ) is continuous, T > 4, T 2 = 2, 3, …, T . The main tool is the Dancer's global bifurcation theorem.