By using Krasnoselskii's fixed point theorem, we study the existence of positive solutions to the three-point summation boundary value problem , , , , where is continuous, is a fixed positive integer, , , and . We show the existence of at least one positive solution if is either superlinear or sublinear.
Thanin Sitthiwirattham. Jessada Tariboon. "Positive Solutions to a Generalized Second-Order Difference Equation with Summation Boundary Value Problem." J. Appl. Math. 2012 1 - 15, 2012. https://doi.org/10.1155/2012/569313