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Approximate Controllability of a Coupled Nonlocal Partial Functional Integro-differential Equations with Impulsive Effects

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Abstract

In this work, we study the approximate controllability problem for a system of nonlocal integro-differential equations with impulsive effects. We start by investigating the existence and uniqueness of solutions for this system. The results are derived using the theory of resolvent operators combined with fixed point theory in a generalized Banach space. Next, we examine approximate controllability without necessarily requiring the nonlinear terms to be uniformly bounded. In particular, we do not impose here the compactness condition for either the resolvent operator or the state-dependent function in the nonlocal condition, as is commonly found in the literature. Finally, we provide an example to demonstrate the abstract results of this work.

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Acknowledgements

We would like to express our sincere gratitude to the anonymous referees and the editor for their careful review and suggestions aimed at improving the quality of this paper.

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Authors and Affiliations

  1. Department of Mathematics, School of Mathematics and Statistics, Nan**g University of Science and Technology, Nan**g, 210094, Jiangsu, People’s Republic of China

    Hamida Litimein & Zhen-You Huang

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

    Sara Litimein & Abdelghani Ouahab

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  1. Hamida Litimein
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  2. Sara Litimein
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  3. Abdelghani Ouahab
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  4. Zhen-You Huang
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Correspondence to Hamida Litimein or Sara Litimein.

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Litimein, H., Litimein, S., Ouahab, A. et al. Approximate Controllability of a Coupled Nonlocal Partial Functional Integro-differential Equations with Impulsive Effects. Qual. Theory Dyn. Syst. 23, 234 (2024). https://doi.org/10.1007/s12346-024-01089-7

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