Existence of Positive Solutions for a Discrete Three-Point Boundary Value Problem - Huting Yuan; Guang Zhang; Hongliang Zhao (Discrete Dynamics in Nature and Society)
A discrete three-point boundary value problem Δ2xk−1+λfk(xk)=0, k=1,2,…,n, x0=0, axl=xn+1, is considered, where 1≤l≤n is a fixed integer, a is a real constant number, and λ is a positive parameter. A characterization of the values of λ is carried out so that the boundary value problem has the positive solutions. Particularly, in this paper the constant a can be negative numbers. The similar results are not valid for the three-point boundary value problem of differential equations.