... BVPs of differential and difference equationshave been studied widely and there are many excellent results see Gai et al. 1, Guo and Tian 2, Henderson and Peterson 3, and Yang et al. 4. ... φφτ>f0− .4.7It follows that, for t ∈ 1,T and 0 < φτ≤ r1,ft, φ>f0− φτ. 4.8 For every y ∈ ∂Kr1 and s ∈ τ 1,T,by3.9, we haveys ... that, for t ∈ 1,T and φ≥r,ft, φ<f∞ 1φ. 4.16We now show that there is r2≥ r, such that, for y ∈ ∂Kr2, Φy≤y. In fact, f ors ∈ 1,T r2≥ Mr/mα and...