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<p>This study focuses on the existence and uniqueness of mild solution for a new class of an abstract neutral integro-differential equation (IDEq) with state-dependent argument (SDA). The concepts of analytic semigroup of bounded linear operators (BLOs) and contraction mapping theorem play a major role in establishing our main results. On the basis of our obtained results we deduce several corollaries. Notably, in this article both Lipschitz and non-Lipschitz solutions of abstract neutral IDEq with SDA are investigated. An example of partial differential equation (DEq) with SDA, is presented at the end.</p>

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Qualitative analysis of an abstract neutral integro-differential equation with state-dependent argument

  • 期刊论文

  • 发表日期：

    2025年11月16日

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  • Bakhtawar Pervaiz,
  • Akbar Zada,
  • Afef Kallekh,
  • Sana Ben Moussa,
  • Ioan-Lucian Popa

摘要

This study focuses on the existence and uniqueness of mild solution for a new class of an abstract neutral integro-differential equation (IDEq) with state-dependent argument (SDA). The concepts of analytic semigroup of bounded linear operators (BLOs) and contraction mapping theorem play a major role in establishing our main results. On the basis of our obtained results we deduce several corollaries. Notably, in this article both Lipschitz and non-Lipschitz solutions of abstract neutral IDEq with SDA are investigated. An example of partial differential equation (DEq) with SDA, is presented at the end.