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<p>The goal of this paper is to deal with the elastic damping system with delay and nonlocal conditions in Banach space. Firstly, Schauder’s fixed point theorem is used to show the existence of mild solutions for our problem. Secondly, a Grönwall-Bellman inequality with delay is given, and the global asymptotic stability of the mild solution is discussed by using this inequality. Finally, a concrete example is given, which shows the feasibility of the abstract results in this paper.</p>

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Asymptotic stability of mild solutions for elastic systems with distributed delay and nonlocal initial conditions

  • 期刊论文

  • 发表日期：

    2025年9月22日

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  • Haide Gou,
  • Yongxiang Li

摘要

The goal of this paper is to deal with the elastic damping system with delay and nonlocal conditions in Banach space. Firstly, Schauder’s fixed point theorem is used to show the existence of mild solutions for our problem. Secondly, a Grönwall-Bellman inequality with delay is given, and the global asymptotic stability of the mild solution is discussed by using this inequality. Finally, a concrete example is given, which shows the feasibility of the abstract results in this paper.