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

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.

MSC:

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

[1] Bainov, D.; Simeonov, P., Integral inequalities and applications, (1992), Kluwer Academic Publishers Dordrecht · Zbl 0759.26012
[2] Cheung, W.S., Some discrete nonlinear inequalities and applications to boundary value problems for difference equations, J. difference equations appl., 10, 2, 213-223, (2004) · Zbl 1045.26007
[3] Engler, H., Global regular solutions for the dynamic antiplane shear problem in nonlinear viscoelasticity, Math. Z., 202, 251-259, (1989) · Zbl 0697.73033
[4] Haraux, A., Nonlinear evolution equations, () · Zbl 0583.35007
[5] Meng, F.W.; Li, W.N., On some new nonlinear discrete inequalities and their applications, J. comput. appl. math., 158, 407-417, (2003) · Zbl 1032.26019
[6] Mitrinović, D.S.; Pečarić, J.K.; Fink, A.M., Inequalities involving functions and their integrals and derivatives, (1991), Kluwer Academic Publishers Dordrecht/Boston/London · Zbl 0744.26011
[7] Pachpatte, B.G., Some new finite difference inequalities, Comput. math. appl., 28, 227, (1994) · Zbl 0809.26009
[8] Pachpatte, B.G., Inequalities applicable in the theory of finite difference equations, J. math. anal. appl., 222, 438-459, (1998) · Zbl 0913.39001
[9] Pachpatte, B.G., On nonlinear finite difference inequalities in two independent variables, Tamkang J. math., 33, 67-75, (2002) · Zbl 1011.26012
[10] Pachpatte, B.G., Inequalities for finite difference equations, (2002), Marcel Dekker New York · Zbl 0987.39001
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