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Globally Exponential Stability of Piecewise Pseudo Almost Periodic Solutions for Neutral Differential Equations with Impulses and Delays

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Abstract

In this paper, a kind of delayed impulsive neutral differential equations (DINDEs) has been studied. By making the use of contraction mapping principle and generalized Gronwall-Bellmain inequality, some novel and sufficient conditions on the existence and uniqueness of the piecewise pseudo almost periodic (PAP) solutions are established. Furthermore, by applying the definition of the globally exponential stability and inequality technology, the globally exponential stability of the piecewise PAP solutions of the addressed DINDE is obtained. The established results of this paper are new and some previous related works are extended and included. Finally, one numerical example is exploited to illustrate the advantages of the established theoretical results.

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Acknowledgements

The authors express their great thanks to the reviewers for their helpful suggestions. This work was jointly supported by the National Natural Science Foundation of China (12001011) and Natural Science Foundation of Anhui Province (2008085QA14).

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Authors and Affiliations

  1. College of Science, Jiujiang University, Jiujiang, 332005, Jiangxi, People’s Republic of China

    Jianxin He & Hongjun Qiu

  2. School of Mathematics and Statistics, Anhui Normal University, Wuhu, 241000, Anhui, People’s Republic of China

    Fanchao Kong

  3. Instituto de Matemáticas, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain

    Juan J. Nieto

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  1. Jianxin He
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  2. Fanchao Kong
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  3. Juan J. Nieto
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  4. Hongjun Qiu
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He, J., Kong, F., Nieto, J.J. et al. Globally Exponential Stability of Piecewise Pseudo Almost Periodic Solutions for Neutral Differential Equations with Impulses and Delays. Qual. Theory Dyn. Syst. 21, 48 (2022). https://doi.org/10.1007/s12346-022-00578-x

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