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Controllability of Mild Solutions for Second-Order Neutral Evolution Equations with State-Dependent Delay

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Abstract

The objective of our research is to demonstrate the controllability of mild solutions for a specific class of second-order neutral functional evolution equations that involve state-dependent delay. To achieve this, we rely on Avramescu’s nonlinear alternative theorem and leverage cosine function theory.

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Data sharing is not applicable to this article as the research primarily involves mathematical analysis and doesn’t entail the generation, collection, or analysis of specific datasets. The results presented in this paper are based on mathematical proofs.

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Funding

Authors were partially supported by the laboratory of mathematics and the faculty of exact sciences at university Djillali Liabes of Sid-Bel-Abbes (Algeria). S. Baghli-Bendimerad’s work will be supported by the General Directorate for Scientific Research and Technological Development (DGRSDT), University-Training Research Projects: C00L03UN220120210002 PRFU 2021 project.

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Authors and Affiliations

  1. Laboratory of Mathematics, Djillali Liabes University of Sidi-Bel-Abbes, Po Box 89, 22000, Sidi-Bel-Abbès, Algeria

    Chahrazed Boudefla, Fatiha Sahraoui & Selma Baghli-Bendimerad

Authors
  1. Chahrazed Boudefla
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  2. Fatiha Sahraoui
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  3. Selma Baghli-Bendimerad
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Contributions

This work is a part of the material of the doctoral dissertation of C. Boudefla. All authors participated in the research and in the drafting of the paper, and reviewed the final version.

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Correspondence to Fatiha Sahraoui.

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Communicated by Daniel Alpay.

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Boudefla, C., Sahraoui, F. & Baghli-Bendimerad, S. Controllability of Mild Solutions for Second-Order Neutral Evolution Equations with State-Dependent Delay. Complex Anal. Oper. Theory 18, 80 (2024). https://doi.org/10.1007/s11785-024-01524-2

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