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Positive Mild Solutions for Damped Elastic Systems with Delay and Nonlocal Conditions in Ordered Banach Space

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Abstract

In this paper, the existence of minimal positive mild solution of a class of structural damped elastic systems with delay and nonlocal conditions on infinite interval are established in ordered Banach spaces. Without assuming the existence of upper and lower solutions of the equation, the conclusions are obtained directly from the characteristics of \(C_{0}-\)semigroup \(T(t)(t\ge 0)\) by using monotone iterative technique and fixed point theorem. At the end, the nonlocal problem of the vibration equation of a concrete simply supported beam is taken as an example to illustrate the feasibility and practical application value of our abstract results.

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Acknowledgements

The authors are most grateful to the editor Professor and anonymous referees for the careful reading of the manuscript and valuable comments that helped in significantly improving an earlier version of this paper.

Funding

This work was supported by NNSF of China (Nos.11661071, 12061062) and The Graduate Research Support project of Northwest Normal University (2021KYZZ01030).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, People’s Republic of China

    Mei Wei & Yongxiang Li

  2. Department of Mathematics, Shanxi Normal University, Linfen, 041000, People’s Republic of China

    Qiang Li

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  1. Mei Wei
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  2. Yongxiang Li
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  3. Qiang Li
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Contributions

M. Wei completed the proof of the main results and the writing of the first draft. Y. Li and Q. Li revised the first draft and put forward some suggestions for revision. All authors read and approved the final manuscript.

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Correspondence to Mei Wei.

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M. Wei, Y. Li and Q. Li declare that they have no competing interests.

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Research supported by NNSF of China (12061062, 11661071), Graduate Research Support project of Northwest Normal University (2021KYZZ01030).

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Wei, M., Li, Y. & Li, Q. Positive Mild Solutions for Damped Elastic Systems with Delay and Nonlocal Conditions in Ordered Banach Space. Qual. Theory Dyn. Syst. 21, 128 (2022). https://doi.org/10.1007/s12346-022-00664-0

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