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Halanay Inequality on Time Scales with Unbounded Coefficients and Its Applications

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Abstract

In the present paper, we obtain a Halanay inequality on time scales with unbounded coefficient for a dynamic problem, which extends a result of Wen et al. (J. Math. Anal. Appl., 347 (2008), 169–178.) to the inequality of integral type on time scales. Moreover, we list two dynamic problems to which the Halanay inequality obtained above can be applied and prove the zero solution of two delay dynamic problems are asymptotically stable. Moreover, it is worth mentioning that the Halanay inequality obtained in the present paper is more precise than the results in [3, 14, 17].

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Acknowledgement

The work was supported by The Key Laboratory of Computational Science of the Guangdong Province and by NSF of Guangdong (Grant: No. S2013010013050). The author would like to thank the anonymous referees for careful reading of the manuscript and their helpful comments. The author thanks B. G. Jia and L. Erbe for the professional guidance and useful comments during the preparation of the paper. Some of the research took place when the author visited the Department of Mathematics of Sun Yat-sen University. He is grateful to the Department of Mathematics for providing nice research conditions.

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  1. Department of Mathematics and Statistics, Lingnan Normal University, Zhanjiang, Guangdong, 524048, People’s Republic of China

    Boqun Ou

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  1. Boqun Ou
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Ou, B. Halanay Inequality on Time Scales with Unbounded Coefficients and Its Applications. Indian J Pure Appl Math 51, 1023–1038 (2020). https://doi.org/10.1007/s13226-020-0447-z

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  • DOI: https://doi.org/10.1007/s13226-020-0447-z

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