... Department of Mathematics, National University of Ireland, Galway, IrelandE-mail address: donal.oregan@nuigalway.ie CONSTRUCTION OF UPPER AND LOWER SOLUTIONS FORSINGULAR DISCRETE INITIAL AND BOUNDARY ... R.P.Agarwal,D.O’Regan,andP.J.Y.Wong,Positive Solutions of Differential, Difference and Integral Equations, Kluwer Academic Publishers, Dordrecht, 1999.[7] P. Habets and F. Zanolin, Upper and lower solutions ... 0,(1.14)then u(k) ≥ 0 for k ∈ [a − 1, b +1]={a − 1,a, , b +1}⊂N+.In Theorems 1.2 and 1.3 the construction of a lower solution α and an upper solutionβ is critical. We present an easily verifiable condition...