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This paper investigates the local and global existence and uniqueness of mild solutions for an abstract second-order differential system with state-driven delay ( \(\mathcal {S}\mathcal {O}\mathcal {D}\mathcal {S}\mathcal {S}\mathcal {D}\mathcal {D}\) ). The study begins by establishing key Lipschitz continuity estimates for the delay term and the associated history map. Following this, the local existence and uniqueness result is demonstrated under suitable conditions. Finally, the paper provides a demonstration of global existence and uniqueness, subject to an inequality constraint.

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Solvability of Abstract Second-Order Differential Systems with State-Driven Delays

  • 会议论文

  • 发表日期：

    2026年

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  • Sandeep Kumar

摘要

This paper investigates the local and global existence and uniqueness of mild solutions for an abstract second-order differential system with state-driven delay ( \(\mathcal {S}\mathcal {O}\mathcal {D}\mathcal {S}\mathcal {S}\mathcal {D}\mathcal {D}\) ). The study begins by establishing key Lipschitz continuity estimates for the delay term and the associated history map. Following this, the local existence and uniqueness result is demonstrated under suitable conditions. Finally, the paper provides a demonstration of global existence and uniqueness, subject to an inequality constraint.