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The Controllability for Second-Order Semilinear Impulsive Systems

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Abstract

This paper studies the controllability of the initial value problems of linear and semilinear second-order impulsive systems. Necessary and sufficient conditions of controllability for linear problems are obtained, and a new rank criterion is presented. We also show semilinear problems are controllable via Krasnoselskii’s fixed point theorem. Finally, two examples are provided to verify the theoretically results.

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Acknowledgements

We would like to thank the referee for his/her important comments.

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Authors and Affiliations

  1. Department of Mathematics, Guizhou University, Guiyang, 550025, Guizhou, China

    Qian Wen & JinRong Wang

  2. Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, 842 48, Mlynská dolina, Bratislava, Slovakia

    Michal Fečkan

  3. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Michal Fečkan

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  1. Qian Wen
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Correspondence to JinRong Wang.

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This work is partially supported by the National Natural Science Foundation of China (12161015), Training Object of High Level and Innovative Talents of Guizhou Province ((2016)4006), Guizhou Data Driven Modeling Learning and Optimization Innovation Team ([2020]5016), the Slovak Research and Development Agency under the contract No. APVV-18-0308, and the Slovak Grant Agency VEGA No. 1/0358/20 and No. 2/0127/20.

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Wen, Q., Fečkan, M. & Wang, J. The Controllability for Second-Order Semilinear Impulsive Systems. Qual. Theory Dyn. Syst. 22, 10 (2023). https://doi.org/10.1007/s12346-022-00717-4

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