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Some delay Gronwall type inequalities on time scales

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Abstract

In this paper, we investigate some delay Gronwall type inequalities on time scales by using Gronwall’s inequality. Our results unify and extend some delay integral inequalities and their corresponding discrete analogues. The inequalities given here can be used as handy tools in the qualitative theory of certain classes of delay dynamic equations on time scales.

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Authors and Affiliations

  1. Department of Mathematics, Binzhou University, Shandong, 256603, China

    Wei-Nian Li

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  1. Wei-Nian Li
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Correspondence to Wei-Nian Li.

Additional information

Supported by the National Natural Science Foundation of China (No. 10971018), the Natural Science Foundation of Shandong Province (No. Y2009A06), China Postdoctoral Science Foundation Funded Project (No. 20080440633), Shanghai Postdoctoral Scientific Program (No. 09R21415200), the Project of Science and Technology of the Education Department of Shandong Province (No. J08LI52), and the Doctoral Foundation of Binzhou University (No. 2006Y01).

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Li, WN. Some delay Gronwall type inequalities on time scales. Acta Math. Appl. Sin. Engl. Ser. 31, 1103–1114 (2015). https://doi.org/10.1007/s10255-015-0534-9

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  • DOI: https://doi.org/10.1007/s10255-015-0534-9

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