The authors provide sufficient conditions for the existence of (at least) three positive solutions of the discrete two-point boundary value problem
where is the usual forward difference operator (note a slightly modified notation used by the authors) and where is continuous. The proof is based on the existence of pairs of discrete lower solutions , and discrete upper solutions , that satisfy the inequalities and . This method is a discrete analog of the authors’ continuous-time results [J. Differ Equations 166, No. 2, 443-454 (2000; Zbl 1013.34017)]. However, in this paper the assumptions do not require and allow being dependent on . If is a function of its second variable only, then the results of this paper are sharp and generalize those of R. J. Avery and A. C. Peterson [Panam. Math. J. 8, No. 3, 1-12 (1998; Zbl 0959.39006)]. This paper will be useful for researchers interested in two-point boundary value problems and/or their positive solutions.