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<p>This paper is dedicated to investigating a semi-linear structural damped elastic system with state-dependent nonlocal condition on an infinite interval. We introduce the fractional power operator and establish several new results on the existence and regularity of mild solutions by applying approximation theory and Schauder fixed point theorem. Eventually, an example of the structural damped beam vibration equation is presented to validate the effectiveness and practicability of the abstract conclusions obtained.</p>

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Existence and Regularity of Solutions to Damping Elastic System with State-Dependent Nonlocal Condition

  • 期刊论文

  • 发表日期：

    2025年6月3日

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  • Mei Wei,
  • Yongxiang Li,
  • Qiang Li

摘要

This paper is dedicated to investigating a semi-linear structural damped elastic system with state-dependent nonlocal condition on an infinite interval. We introduce the fractional power operator and establish several new results on the existence and regularity of mild solutions by applying approximation theory and Schauder fixed point theorem. Eventually, an example of the structural damped beam vibration equation is presented to validate the effectiveness and practicability of the abstract conclusions obtained.