P A POSITIVE SOLUTIONS OF SUMMATION BOUNDARY VALUE PROBLEM FOR A GENERALIZED SECOND-ORDER DIFFERENCE EQUATION

Abstract

Abstract: In this paper, by using Krasnoselskii's fixed point theorem, we study the existence of positive solutions to the three-point summation boundary value problem ∆ 2 y(t − 1) + a(t)f (y(t)) = 0, t ∈ {1, 2, ..., T }, where f is continuous, T ≥ 3 is a fixed positive integer, η ∈ {1, 2, ..., T − 1}, and ∆y(t − 1) = y(t) − y(t − 1) is the forward difference operator. We show the existence of at least one positive solution if f is neither superlinear and sublinear by applying the fixed point theorem in cones