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Some nonlinear Gronwall–Bellman type retarded integral inequalities with power and their applications

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  • Li, Zizun
  • Wang, Wu-Sheng

Abstract

The purpose of this paper is to establish some new retarded integral inequalities of Gronwall-Bellman type, which generalizes some known integral inequalities. We use two lemmas to simplify the complex inequalities and give an upper bound estimation of the unknown function. The inequalities given here can be used in the analysis of the qualitative properties of certain classes of differential equations and integral equations. We apply our results to the boundedness of the solutions of integral equations and differential system.

Suggested Citation

  • Li, Zizun & Wang, Wu-Sheng, 2019. "Some nonlinear Gronwall–Bellman type retarded integral inequalities with power and their applications," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 839-852.
    • Handle: RePEc:eee:apmaco:v:347:y:2019:i:c:p:839-852
    DOI: 10.1016/j.amc.2018.10.019
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    References listed on IDEAS

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    1. Abdeldaim, A. & El-Deeb, A.A., 2015. "On generalized of certain retarded nonlinear integral inequalities and its applications in retarded integro-differential equations," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 375-380.
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