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Some discrete nonlinear inequalities and applications to boundary value problems for difference equations. (English) Zbl 1045.26007

The main results (i.e., Theorems 2.1 and 2.2 ) given in this paper are the ramifications of the inequalities due to the reviewer given in his book: “Inequalities for finite difference equations” (2002; Zbl 0987.39001) (see, Theorem 5.2.1, p.387 and Theorem 5.4.8, part(c2), p. 432). For a number of discrete nonlinear inequalities and their applications, see the book noted above.

MSC:

26D15 Inequalities for sums, series and integrals
39A10 Additive difference equations
39A70 Difference operators
47J20 Variational and other types of inequalities involving nonlinear operators (general)

Citations:

Zbl 0987.39001
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References:

[1] Agarwal RP, Difference Equations and Inequalities (2000)
[2] Bainov D, Integral Inequalities and Applications (1992)
[3] Beckenbach EF, Inequalities (1961)
[4] Bellman R, Duke Math. J. 10 pp 643– (1943) · Zbl 0061.18502
[5] Bihari I, Acta Math. Acad. Sci. Hungar. 7 pp 71– (1956) · Zbl 0070.08201
[6] Cheung WS, J. Math. Anal. Appl. 178 pp 438– (1993) · Zbl 0796.26007
[7] Cheung WS, J. Concrete Appl. Math. (2003)
[8] Gronwall TH, Ann. Math. 20 pp 292– (1919) · JFM 47.0399.02
[9] Haraux H, Nonlinear Evolution Equation: Global Behavior of Solutions 841 (1981)
[10] Ma QM, J. Math. Anal. Appl. 252 pp 864– (2000) · Zbl 0974.26015
[11] Ma QM, Period. Math. Hungar. 44 pp 225– (2002) · Zbl 1006.26011
[12] Mitrinović DS, Analytic Inequalities (1970) · Zbl 0199.38101
[13] Mitrinović DS, Inequalities Involving Functions and their Integrals and Derivatives (1991)
[14] Ou-Iang L, Shuxue Jinzhan 3 pp 409– (1957)
[15] Pachpatte BG, J. Math. Anal. Appl. 267 pp 48– (2002) · Zbl 0996.26008
[16] Pachpatte BG, Inequalities for Differential and Integral Equations (1998)
[17] Pachpatte BG, J. Math. Anal. Appl. 251 pp 736– (2000) · Zbl 0987.26010
[18] Pachpatte BG, J. Math. Anal. Appl. 189 pp 128– (1995) · Zbl 0824.26010
[19] Pang PYH, J. Math. Anal. Appl. 194 pp 569– (1995) · Zbl 0845.26009
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