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Controllability of Second Order Impulsive Neutral Functional Differential Inclusions with Infinite Delay

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  • Dimplekumar N. Chalishajar

    (Virginia Military Institute)

Abstract

This paper is concerned with controllability of a partial neutral functional differential inclusion of second order with impulse effect and infinite delay. We introduce a new phase space to prove the controllability of an inclusion which consists of an impulse effect with infinite delay. We claim that the phase space considered by different authors is not correct. We establish the controllability of mild solutions using a fixed point theorem for contraction multi-valued maps and without assuming compactness of the family of cosine operators.

Suggested Citation

  • Dimplekumar N. Chalishajar, 2012. "Controllability of Second Order Impulsive Neutral Functional Differential Inclusions with Infinite Delay," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 672-684, August.
    • Handle: RePEc:spr:joptap:v:154:y:2012:i:2:d:10.1007_s10957-012-0025-6
    DOI: 10.1007/s10957-012-0025-6
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    Cited by:

    1. Elimhan N. Mahmudov, 2018. "Optimization of Mayer Problem with Sturm–Liouville-Type Differential Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 177(2), pages 345-375, May.
    2. Dimplekumar Chalishajar & Annamalai Anguraj & Kandasamy Malar & Kulandhivel Karthikeyan, 2016. "A Study of Controllability of Impulsive Neutral Evolution Integro-Differential Equations with State-Dependent Delay in Banach Spaces," Mathematics, MDPI, vol. 4(4), pages 1-16, October.
    3. Elimhan N. Mahmudov, 2022. "Optimization of Higher-Order Differential Inclusions with Special Boundary Value Conditions," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 36-55, January.
    4. Jia Wei He & Yong Liang & Bashir Ahmad & Yong Zhou, 2019. "Nonlocal Fractional Evolution Inclusions of Order α ∈ (1,2)," Mathematics, MDPI, vol. 7(2), pages 1-17, February.
    5. Dimplekumar N. Chalishajar & Kulandhivel Karthikeyan & Annamalai Anguraj, 2016. "Existence of Semi Linear Impulsive Neutral Evolution Inclusions with Infinite Delay in Frechet Spaces," Mathematics, MDPI, vol. 4(2), pages 1-17, April.
    6. Eduardo Hernández & Donal O’Regan & Krishnan Balachandran, 2013. "Comments on Some Recent Results on Controllability of Abstract Differential Problems," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 292-295, October.

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