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Approximate Controllability of Non-autonomous Second Order Impulsive Functional Evolution Equations in Banach Spaces

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Abstract

This article investigates the approximate controllability of second order non-autonomous functional evolution equations involving non-instantaneous impulses and nonlocal conditions. First, we discuss the approximate controllability of second order linear system in detail, which lacks in the existing literature. Then, we derive sufficient conditions for approximate controllability of our system in separable reflexive Banach spaces via linear evolution operator, resolvent operator conditions, and Schauder’s fixed point theorem. Moreover, in this paper, we define proper identification of resolvent operator in Banach spaces. Finally, we provide two concrete examples to validate our results.

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Acknowledgements

S. Arora would like to thank Council of Scientific and Industrial Research, New Delhi, Government of India (File No. 09/143(0931)/2013 EMR-I), for financial support to carry out his research work and Department of Mathematics, Indian Institute of Technology Roorkee (IIT Roorkee), for providing stimulating scientific environment and resources. J. Dabas would like to thank the Department of Atomic Energy (DAE), Mumbai, Government of India, project (file no-02011/12/2021 NBHM(R.P)/R &D II/7995).

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Authors and Affiliations

  1. Department of Applied Mathematics and Scientific Computing, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, 247667, India

    Sumit Arora, Soniya Singh & Jaydev Dabas

  2. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, 247667, India

    Manil T. Mohan

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  1. Sumit Arora
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Arora, S., Singh, S., Mohan, M.T. et al. Approximate Controllability of Non-autonomous Second Order Impulsive Functional Evolution Equations in Banach Spaces. Qual. Theory Dyn. Syst. 22, 31 (2023). https://doi.org/10.1007/s12346-022-00718-3

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