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<p>In this study, we investigate the existence of solutions and an optimal state-control pair for a specific category of non-autonomous impulsive integrodifferential equations that incorporate nonlocal conditions. The linear part of these equations varies with time and leads to the formation of a linear evolution system. Utilizing Krasnoselskii’s fixed point Theorem in conjunction with Grimmer’s resolvent operator theory, we establish proofs for mild solution. Additionally, we explore the existence of an optimal state-control pair related to the constrained Lagrange problem <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\left( \mathcal {P}\right) \)</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mi mathvariant="script">P</mi> </mfenced> </math></EquationSource> </InlineEquation> associated with the control system under review. The main results are obtained by leveraging certain compactness properties of relevant operators along with techniques involving minimizing sequences without relying on Lipschitz continuity for the nonlinear component. For illustration, we provide an example at the conclusion of this work.</p>

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Existence and optimal controls of non-autonomous impulsive integrodifferential evolution equations with nonlocal conditions

  • 期刊论文

  • 发表日期：

    2026年6月15日

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  • Nafy Ngom,
  • Papa Ali Thiam,
  • Khalil Ezzinbi,
  • Mamadou Abdoul Diop

摘要

In this study, we investigate the existence of solutions and an optimal state-control pair for a specific category of non-autonomous impulsive integrodifferential equations that incorporate nonlocal conditions. The linear part of these equations varies with time and leads to the formation of a linear evolution system. Utilizing Krasnoselskii’s fixed point Theorem in conjunction with Grimmer’s resolvent operator theory, we establish proofs for mild solution. Additionally, we explore the existence of an optimal state-control pair related to the constrained Lagrange problem \(\left( \mathcal {P}\right) \) P associated with the control system under review. The main results are obtained by leveraging certain compactness properties of relevant operators along with techniques involving minimizing sequences without relying on Lipschitz continuity for the nonlinear component. For illustration, we provide an example at the conclusion of this work.