Discrete non-linear inequalities and applications to boundary value problems.

*(English)*Zbl 1116.26016The authors establish explicit upper bounds for some nonlinear discrete inequalities of Gronwall-Bellman-Ou-Yang type. The results are further generalizations of inequalities of this type of W.-S. Cheung [J. Difference Equ. Appl. 10, No. 2, 213–223 (2004; Zbl 1045.26007)] and B. G. Pachpatte [J. Math. Anal. Appl. 189, No. 1, 128–144 (1995; Zbl 0824.26010) and JIPAM, J. Inequal. Pure Appl. Math. 3, No. 2, Paper No. 18 (2002; Zbl 0994.26017)]. Applications of the results obtained to study the boundedness, uniqueness, and continuous dependence of solutions of certain discrete boundary value problems for difference equations are given.

Reviewer: James Adedayo Oguntuase (Abeokuta)

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\textit{W.-S. Cheung} and \textit{J. Ren}, J. Math. Anal. Appl. 319, No. 2, 708--724 (2006; Zbl 1116.26016)

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