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Existence of Semi Linear Impulsive Neutral Evolution Inclusions with Infinite Delay in Frechet Spaces

Author

Listed:
  • Dimplekumar N. Chalishajar

    (Department of Applied Mathematics, Virginia Military Institute (VMI), 431 Mallory Hall, Lexington, VA 24450, USA)

  • Kulandhivel Karthikeyan

    (Department of Mathematics, KSR College of Technology, Tiruchengode 637215, India
    These authors contributed equally to this work.)

  • Annamalai Anguraj

    (Department of Mathematics, PSG College of Arts and Science, Coimbatore 641014 , India
    These authors contributed equally to this work.)

Abstract

In this paper, sufficient conditions are given to investigate the existence of mild solutions on a semi-infinite interval for first order semi linear impulsive neutral functional differential evolution inclusions with infinite delay using a recently developed nonlinear alternative for contractive multivalued maps in Frechet spaces due to Frigon combined with semigroup theory. The existence result has been proved without assumption of compactness of the semigroup. We introduced a new phase space for impulsive system with infinite delay and claim that the phase space considered by different authors are not correct.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:4:y:2016:i:2:p:23-:d:67615
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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. John R. Graef & Abdelghani Ouahab, 2006. "Some existence and uniqueness results for first-order boundary value problems for impulsive functional differential equations with infinite delay in Fréchet spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2006, pages 1-16, July.
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