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On neutral integrodifferential equations with state-dependent delay in Banach spaces

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Abstract

In this work, we investigate the existence of mild solution for semilinear integro-differential systems and semilinear neutral integro-differential systems with state-dependent delay in Banach spaces. Using Mönch’s fixed point theorem, the theory of Grimmer’s resolvent operator and the idea of measures of non-compactness, we prove the existence results. At the end, an example is given to further illustrate the conclusions drawn from the theoretical study.

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Authors and Affiliations

  1. Université Gaston Berger de Saint-Louis, UFR SAT Département de Mathématiques, B.P. 234, Saint-Louis, Senegal

    Mbarack Fall, Aziz Mané & Mamadou Abdoul Diop

  2. UMMISCO UMI 209 IRD/UPMC, Bondy, France

    Mamadou Abdoul Diop

  3. Department of Mathematics, PSG College of Arts and Science, Coimbatore, 641014, India

    Ramkumar Kasinathan & Ravikumar Kasinathan

Authors
  1. Mbarack Fall
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  2. Aziz Mané
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  3. Ramkumar Kasinathan
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  4. Ravikumar Kasinathan
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  5. Mamadou Abdoul Diop
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Correspondence to Mamadou Abdoul Diop.

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Fall, M., Mané, A., Kasinathan, R. et al. On neutral integrodifferential equations with state-dependent delay in Banach spaces. Afr. Mat. 35, 52 (2024). https://doi.org/10.1007/s13370-024-01193-6

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  • DOI: https://doi.org/10.1007/s13370-024-01193-6

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