Triple Monotone Positive Solutions for Higher Order Discrete Boundary Value Problems

Green’s function for a class of 2 n th order discrete boundary value problems is given, and a completely continuous operator on a cone is constructed by the Green’s function. Two nonnegative continuous concave functionals and three nonnegative continuous convex functionals on the cone are defined. Using the five functionals fixed point theorem, the existence of three monotone positive solutions for the boundary value problems is studied.