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Periodic Mild Solutions of Infinite Delay not Instantaneous Impulsive Evolution Inclusions

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Abstract

This paper deals with the existence of periodic mild solutions for a class of functional evolution inclusions. We use a multivalued fixed point theorem in Banach spaces combined with the technique of measure of noncompactness. We show that the Poincaré operator is a condensing operator with respect to Kuratowski’s measure of noncompactness in a determined phase space, and then derive periodic solutions from bounded solutions by using Sadovskii’s fixed point theorem.

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Acknowledgements

The authors are grateful to the referees for the careful reading of the paper and for their helpful remarks.

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Authors and Affiliations

  1. Department of Mathematics, University of Saïda – Dr. Moulay Tahar, P.O. Box 138, EN-Nasr, 20000, Saïda, Algeria

    Saïd Abbas

  2. Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, P.O. Box 89, Sidi Bel-Abbès, 22000, Algeria

    Mouffak Benchohra

  3. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia

    Mouffak Benchohra

  4. NEERLab, Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, MD, 21252, USA

    Gaston N’Guérékata

Authors
  1. Saïd Abbas
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  2. Mouffak Benchohra
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  3. Gaston N’Guérékata
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Correspondence to Gaston N’Guérékata.

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Abbas, S., Benchohra, M. & N’Guérékata, G. Periodic Mild Solutions of Infinite Delay not Instantaneous Impulsive Evolution Inclusions. Vietnam J. Math. 50, 287–299 (2022). https://doi.org/10.1007/s10013-021-00487-7

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  • DOI: https://doi.org/10.1007/s10013-021-00487-7

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