Single And Multiple Positive Solutions To Second-order Discrete Periodic Boundary Value Problems

In this paper, we consider the following periodic boundary value problem: where is a desired solution. As usual, â–³ denotes the forward difference operator defined byMany authors have investigated the existence of positive periodic solutions for differential equations with periodic coefficients and the existence of positive solutions for boundary value problems (in the continuous case). However, there are few results on the discrete case [1-4, 23,24]. Recently, the authors of [4] considered the BVP (1.1) and (1.2) and gave the sufficient conditions about the existence of single and multiple solutions by employing the norm-type expansion and compression theorem due to Krasnoselskii.This paper presents a new existence theory for single and multiple positive solutions to a kind of second-order discrete periodic boundary value problems by employing a fixed point theorem in cones. We report some new results about nonlinear differential equations on a finite discrete segment with periodic boundary conditions.