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Positive Periodic Solutions of Coupled Singular Rayleigh Systems

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Abstract

This paper mainly aims to investigate the positive periodic solutions for coupled singular Rayleigh systems. In order to establish the coupled structure, the basic framework of graph theory is employed. By means of Lyapunov method, inequality techniques and a classical consequence of Mawhin’s continuation theorem, some sufficient criterion for the positive periodic solutions has been provided. After that, taken the effects of the delays into account and without imposing more conditions, we further study the positive periodic solutions for a kind of coupled singular Rayleigh system with delays. Here not only the structure is more general than the existing works but the conditions imposed are concise. Consequently, compared with the previous results on the singular systems and coupled systems, the results we established are more generalized and some previous ones can been complemented and improved. Finally, the effectiveness of the established results are validated via an numerical example.

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Acknowledgements

The authors thank the anonymous reviewers for their insightful suggestions which improved this work significantly. This work was jointly supported by the National Natural Science Foundation of China (No. 11671013), Anhui Provincial Natural Science Foundation (No. 2008085QA14) and the Talent Foundation of Anhui Normal University (No. 751965).

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Authors and Affiliations

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

    Fanchao Kong & Feng Liang

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

    Juan J. Nieto

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  1. Fanchao Kong
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  2. Feng Liang
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  3. Juan J. Nieto
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Correspondence to Fanchao Kong or Feng Liang.

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Kong, F., Liang, F. & Nieto, J.J. Positive Periodic Solutions of Coupled Singular Rayleigh Systems. Qual. Theory Dyn. Syst. 19, 88 (2020). https://doi.org/10.1007/s12346-020-00427-9

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