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A Study of Controllability of Impulsive Neutral Evolution Integro-Differential Equations with State-Dependent Delay in Banach Spaces

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  • Dimplekumar Chalishajar

    (Department of Applied Mathematics, 435 Mallory Hall, Virginia Military Institute (VMI), Lexington, VA 24450, USA)

  • Annamalai Anguraj

    (Department of Mathematics, PSG College of Arts and Science, Coimbatore, Tamil Nadu 641014, India)

  • Kandasamy Malar

    (Department of Mathematics, Erode Arts and Science College, Erode, Tamil Nadu 638009, India)

  • Kulandhivel Karthikeyan

    (Department of Mathematics, K.S.R. College of Technology, Tiruchengode, Tamil Nadu 637215, India)

Abstract

In this paper, we study the problem of controllability of impulsive neutral evolution integro-differential equations with state-dependent delay in Banach spaces. The main results are completely new and are obtained by using Sadovskii’s fixed point theorem, theory of resolvent operators, and an abstract phase space. An example is given to illustrate the theory.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:4:y:2016:i:4:p:60-:d:80841
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    References listed on IDEAS

    as
    1. 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.
    2. X. Zhang, 2000. "Exact Controllability of Semilinear Evolution Systems and Its Application," Journal of Optimization Theory and Applications, Springer, vol. 107(2), pages 415-432, November.
    3. K. Balachandran & J.P. Dauer, 2002. "Controllability of Nonlinear Systems in Banach Spaces: A Survey," Journal of Optimization Theory and Applications, Springer, vol. 115(1), pages 7-28, October.
    4. Balasubramaniam, P. & Tamilalagan, P., 2015. "Approximate controllability of a class of fractional neutral stochastic integro-differential inclusions with infinite delay by using Mainardi’s function," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 232-246.
    5. B. Radhakrishnan & K. Balachandran, 2011. "Controllability Results for Second Order Neutral Impulsive Integrodifferential Systems," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 589-612, December.
    6. Xuetao Yang & Quanxin Zhu & Zhangsong Yao, 2014. "p th Moment Exponential Stability of Nonlinear Hybrid Stochastic Heat Equations," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-7, August.
    Full references (including those not matched with items on IDEAS)

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