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Controllability of non-autonomous nonlinear differential system with non-instantaneous impulses

  • Muslim Malik
  • Rajesh Dhayal
  • Syed AbbasEmail author
  • Avadhesh Kumar
Original Paper
  • 241 Downloads

Abstract

In this paper, we applied the Rothe’s fixed point theorem to study the controllability of non-autonomous nonlinear differential system with non-instantaneous impulses in the space \(\mathbb {R}^{n}\). Also, we established the sufficient conditions for the controllability of the integro-differential equation as well as nonlocal problem. Finally, we have given an example to illustrate the application of these proposed results.

Keywords

Controllability Non-autonomous differential system Non-instantaneous impulses Rothe’s fixed point theorem 

Mathematics Subject Classification

93B05 34K45 34G20 

Notes

Acknowledgements

We are thankful to the anonymous reviewers for their constructive comments and suggestions which help us to improve the manuscript.

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Copyright information

© Springer-Verlag Italia S.r.l. 2017

Authors and Affiliations

  • Muslim Malik
    • 1
  • Rajesh Dhayal
    • 1
  • Syed Abbas
    • 1
    Email author
  • Avadhesh Kumar
    • 1
  1. 1.School of Basic SciencesIndian Institute of Technology MandiKamandIndia

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