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Approximate controllability of semilinear system involving state-dependent delay via fundamental solution

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Abstract

This article studies approximate controllability for a new class of semilinear control systems involving state-dependent delay in Hilbert space setting. We formulate some new sufficient conditions which ensure the existence of mild solution for the considered system via the Schauder fixed point theorem. We use the theory of fundamental solution and fractional powers of operator, to establish our major results. At last, two examples are constructed to substantiate the application of obtained results.

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Acknowledgements

We are very thankful to the anonymous reviewer and the Editor for their valuable comments and suggestions which help us to improve the manuscript. The first author is supported by the Council of Scientific & Industrial Research (CSIR), India (Grant No.: 18/12/2016(ii)EU-V).

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  1. Department of Mathematics, University of Delhi, New Delhi, Delhi, 110007, India

    Syed Mohammad Abdal & Surendra Kumar

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  1. Syed Mohammad Abdal
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Abdal, S.M., Kumar, S. Approximate controllability of semilinear system involving state-dependent delay via fundamental solution. Ricerche mat 69, 261–282 (2020). https://doi.org/10.1007/s11587-019-00461-z

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