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New Monch–Krasnosel’skii type fixed point theorems applied to solve neutral partial integrodifferential equations without compactness

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Abstract

In this paper, we show the existence of mild solutions for a class of neutral partial integrodifferential equations with lack of compactness. The results are obtained using noncompact resolvent operators and a new fixed point theorem of Monch-Krasnosel’skii type. Our results are applied to a large variety of partial differential equations in which memory effects are considered. An example is provided at the end of the paper to illustrate the main results of this work.

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Acknowledgements

The authors are very grateful to the referee for his valuable suggestions and comments.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, B. P. 2390, Marrakesh, Morocco

    Khalil Ezzinbi

  2. Department of Mathematics, University of Gafsa Faculty of Sciences, B. P. 2112, Gafsa, Tunisia

    Saifeddine Ghnimi

  3. National School of Applied Science, Cadi Ayyad University, Marrakesh, Morocco

    Mohamed Aziz Taoudi

Authors
  1. Khalil Ezzinbi
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  2. Saifeddine Ghnimi
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  3. Mohamed Aziz Taoudi
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Correspondence to Mohamed Aziz Taoudi.

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Ezzinbi, K., Ghnimi, S. & Taoudi, M.A. New Monch–Krasnosel’skii type fixed point theorems applied to solve neutral partial integrodifferential equations without compactness. J. Fixed Point Theory Appl. 22, 73 (2020). https://doi.org/10.1007/s11784-020-00810-8

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