Positive Solution of Nonlinear Two-order Three-point Boundary Value Problem for Difference Equation with Change of Sign

摘要

In this paper we investigate the existence of positive solution of the following discrete two-order three-point boundary value problem △~2x_(k-1)+h(k)f(x_k)=0, k ∈ [1, n]; x_0=0, ax_1=x_(n+1), Wher n ∈ [(2, ∞], l ∈ [1, n], 0＜a＜1, (1-a)l≥2, f ∈ C(R~+, R~+) and h(t) is sign-changing on [1, n]. By using the fixed-point index theory, the existence of positive solutions for the above boundary value problem is obtained.