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Nonlinear integral inequalities in two independent variables on time scales. (English) Zbl 1213.26028

Summary: We investigate some nonlinear integral inequalities in two independent variables on time scales. Our results unify and extend some integral inequalities and their corresponding discrete analogues which established by Pachpatte. The inequalities given here can be used as handy tools to study the properties of certain partial dynamic equations on time scales.

MSC:

26D15 Inequalities for sums, series and integrals
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[1] Bohner M, Peterson A: Dynamic Equations on Time Scales: An Introduction with Applications. Birkhäuser, Boston, Mass, USA; 2001:x+358. · Zbl 0978.39001 · doi:10.1007/978-1-4612-0201-1
[2] Bohner M, Peterson A (Eds): Advances in Dynamic Equations on Time Scales. Birkhäuser, Boston, Mass, USA; 2003:xii+348. · Zbl 1025.34001
[3] Agarwal R, Bohner M, Peterson A: Inequalities on time scales: a survey.Mathematical Inequalities & Applications 2001,4(4):535-557. · Zbl 1021.34005 · doi:10.7153/mia-04-48
[4] Akin-Bohner E, Bohner M, Akin F: Pachpatte inequalities on time scales.Journal of Inequalities in Pure and Applied Mathematics 2005,6(1, article 6):1-23. · Zbl 1086.34014
[5] Li WN: Some new dynamic inequalities on time scales.Journal of Mathematical Analysis and Applications 2006,319(2):802-814. 10.1016/j.jmaa.2005.06.065 · Zbl 1103.34002 · doi:10.1016/j.jmaa.2005.06.065
[6] Wong F-H, Yeh C-C, Hong C-H: Gronwall inequalities on time scales.Mathematical Inequalities & Applications 2006,9(1):75-86. · Zbl 1091.26020 · doi:10.7153/mia-09-08
[7] Li WN, Sheng W: Some nonlinear dynamic inequalities on time scales.Proceedings of the Indian Academy of Sciences Mathematical Sciences 2007,117(4):545-554. 10.1007/s12044-007-0044-7 · Zbl 1149.34308 · doi:10.1007/s12044-007-0044-7
[8] Li WN: Some Pachpatte type inequalities on time scales.Computers & Mathematics with Applications 2009,57(2):275-282. 10.1016/j.camwa.2008.09.040 · Zbl 1165.39301 · doi:10.1016/j.camwa.2008.09.040
[9] Li, WN, Bounds for certain new integral inequalities on time scales, No. 2009, 16 (2009) · Zbl 1177.26041
[10] Anderson DR: Dynamic double integral inequalities in two independent variables on time scales.Journal of Mathematical Inequalities 2008,2(2):163-184. · Zbl 1170.26306 · doi:10.7153/jmi-02-16
[11] Anderson DR: Nonlinear dynamic integral inequalities in two independent variables on time scale pairs.Advances in Dynamical Systems and Applications 2008,3(1):1-13.
[12] Ahlbrandt CD, Morian Ch: Partial differential equations on time scales.Journal of Computational and Applied Mathematics 2002,141(1-2):35-55. 10.1016/S0377-0427(01)00434-4 · Zbl 1134.35314 · doi:10.1016/S0377-0427(01)00434-4
[13] Hoffacker J: Basic partial dynamic equations on time scales.Journal of Difference Equations and Applications 2002,8(4):307-319. 10.1080/1026190290017379 · Zbl 1003.39018 · doi:10.1080/1026190290017379
[14] Jackson B: Partial dynamic equations on time scales.Journal of Computational and Applied Mathematics 2006,186(2):391-415. 10.1016/j.cam.2005.02.011 · Zbl 1081.39013 · doi:10.1016/j.cam.2005.02.011
[15] Bohner M, Guseinov GSh: Partial differentiation on time scales.Dynamic Systems and Applications 2004,13(3-4):351-379. · Zbl 1090.26004
[16] Bohner M, Guseinov GSh: Double integral calculus of variations on time scales.Computers & Mathematics with Applications 2007,54(1):45-57. 10.1016/j.camwa.2006.10.032 · Zbl 1131.49019 · doi:10.1016/j.camwa.2006.10.032
[17] Wang, P.; Li, P., Monotone iterative technique for partial dynamic equations of first order on time scales, No. 2008, 7 (2008) · Zbl 1149.35334
[18] Mitrinović DS: Analytic Inequalities, Die Grundlehren der mathematischen Wissenschaften. Volume 16. Springer, New York, NY, USA; 1970:xii+400.
[19] Pachpatte BG: Integral and Finite Difference Inequalities and Applications, North-Holland Mathematics Studies. Volume 205. Elsevier Science B.V., Amsterdam, The Netherlands; 2006:x+309. · Zbl 1104.26015
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