Some new nonlinear difference inequalities and their applications. (English) Zbl 1121.26019

Ma, Qing-Hua; Cheung, Wing-Sum

J. Comput. Appl. Math. 202, No. 2, 339-351 (2007).

The aim of the paper is to establish some new difference inequalities in two independent variables. A suitable choice of parameters involved gives discrete Gronwall-Ou-Iang type inequalities, cf. B. G. Pachpatte [J. Math. Anal. Appl. 222, No. 2, 438–459 (1998; Zbl 0913.39001)], and Haraux-Engler type inequalities, cf. A. Haraux [“Nonlinear evolution equations – global behavior of solutions” (1981; Zbl 0461.35002)] and H. Engler [Math. Z. 202, No. 2, 251–259 (1989; Zbl 0697.73033)] in two variables. Results also cover some inequalities proved by B. G. Pachpatte [“Inequalities for finite difference equations” (2002; Zbl 0987.39001)]. Applications to partial difference equations are given.

Reviewer: Bohumír Opic (Praha)

MSC:

26D15	Inequalities for sums, series and integrals
26D20	Other analytical inequalities

Keywords:

finite difference inequality; two independent variables; difference equations

Citations:

Zbl 0913.39001; Zbl 0461.35002; Zbl 0697.73033; Zbl 0987.39001

References:

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