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Positive Periodic Solutions for a Kind of First-Order Singular Differential Equation Induced by Impulses

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Abstract

By using the continuation theorem due to Mawhin and Gaines, the sufficient conditions ensuring the existence of positive periodic solutions for a kind of first-order singular differential equation induced by impulses. Some recent results in the literature are improved.

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Acknowledgements

The authors thank the anonymous reviewers for their insightful suggestions which improved this work significantly. The research was supported by the National Natural Science Foundation of China (Grant Nos. 11661037,11471109), Hunan Provincial Natural Science Foundation of China (Grant No. 2016JJ6122), Jishou University Doctor Science Foundation (Grant No. jsdxxcfxbskyxm201504) and Hunan Provincial Innovation Foundation For Postgraduate.

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  1. Department of Mathematics, Hunan Normal University, Changsha, 410081, Hunan, People’s Republic of China

    Fanchao Kong & Zhiguo Luo

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  1. Fanchao Kong
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  2. Zhiguo Luo
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Correspondence to Fanchao Kong.

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Kong, F., Luo, Z. Positive Periodic Solutions for a Kind of First-Order Singular Differential Equation Induced by Impulses. Qual. Theory Dyn. Syst. 17, 375–386 (2018). https://doi.org/10.1007/s12346-017-0239-y

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