Generalization of a retarded Gronwall-like inequality and its applications

Agarwal, Ravi P.; Deng, Shengfu; Zhang, Weinian

doi:10.1016/j.amc.2004.04.067

Cited by 141 publications

(74 citation statements)

References 8 publications

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“…for all t I. Lemma 6 (see [5]). Let C(R + ,R + ) be a increasing function, u,a,f C([t 0 ,T),R + ), a (t) be a increasing function, and a C 1 ([t 0 ,T), [t 0 ,T)) be nondecreasing with a(t) ≤ t on [t 0 ,T) where T (0,∞) is a constant.…”

Section: Lemma 5 (Abdeldaim and Yakoutmentioning

confidence: 99%

Some retarded nonlinear integral inequalities and their applications in retarded differential equations

Wang

2012

J Inequal Appl

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In this article, we discuss some generalized retarded nonlinear integral inequalities, which not only include nonlinear compound function of unknown function but also include retard items, and give upper bound estimation of the unknown function by integral inequality technique. This estimation can be used as tool in the study of differential equations with the initial conditions. 2000 MSC: 26D10; 26D15; 26D20; 34A12; 34A40.

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Section: Lemma 5 (Abdeldaim and Yakoutmentioning

confidence: 99%

Some retarded nonlinear integral inequalities and their applications in retarded differential equations

Wang

2012

J Inequal Appl

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“…1 School of Science, Southwest University of Science and Technology, Mianyang, Sichuan 621010, P.R. China.…”

Section: Applicationsmentioning

confidence: 99%

On nonlinear discrete weakly singular inequalities and applications to Volterra-type difference equations

2013

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“…During the past few years there have been a number of papers written on discrete versions of Gronwall-Bellman-type inequalities. For example, see [1][2][3][4][5][6][7][8][9][10][11][12][13]. Found in [6], the unknown function u in the fundamental form of sumdifference inequality …”

Section: Introductionmentioning

confidence: 99%

Discrete Nonlinear Inequalities and Applications to Boundary Value Problems for Difference Equations

Sun¹

2013

Proceedings of the 2013 International Conference on Advanced Computer Science and Electronics Information

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-In this paper, some new discrete nonlinear inequalities with two variables are established and explicit bounds on the unknown function are derived. These inequalities generalize former results and can be used as handy tools to study the qualitative as well as the quantitative properties of certain partial difference equations. Example of applying these inequalities to derive the properties of boundary Value problems for difference equations is also given.

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Generalization of a retarded Gronwall-like inequality and its applications

Cited by 141 publications

References 8 publications

Some retarded nonlinear integral inequalities and their applications in retarded differential equations

Some retarded nonlinear integral inequalities and their applications in retarded differential equations

On nonlinear discrete weakly singular inequalities and applications to Volterra-type difference equations

Discrete Nonlinear Inequalities and Applications to Boundary Value Problems for Difference Equations

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