Skip to main content
SpringerLink
Log in

Existence results for quasilinear random impulsive abstract differential inclusions in Hilbert space

  • Original Research Paper
  • Published:
The Journal of Analysis Aims and scope Submit manuscript

Abstract

In this paper, the existence of solutions for quasilinear random impulsive neutral functional differential inclusions are studied for both convex and non-convex cases in a real separable Hilbert space. The results are obtained by using the Martelli, Covitz and Nadler’s fixed point theorems and semigroup theory. An example is given as an application for the abstract results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Akhmetov, M.U., and A. Zafer. 2000. Stability of Zero solution of Impulsive differential Equations by the Lyapunov second method. Journal of Mathematics and Analysis with Applications 248: 69–82.

    Article  MathSciNet  MATH  Google Scholar 

  2. Bahuguna, D. 1995. Quasilinear integrodifferential equations in Banach spaces. Nonlinear Analysis 24: 175–183.

    Article  MathSciNet  MATH  Google Scholar 

  3. Hernndez, E., M. Rabello, and H.R. Henriquez. 2007. Existence of solutions for impulsive partial neutral functional differential equations. Journal of Mathematics and Analysis with Applications 331: 1135–1158.

    Article  MathSciNet  MATH  Google Scholar 

  4. Kato, T. 1975. Quasilinear equations of evolution with applications to partial differential equations. Lecture Notes in Mathematics 448: 25–70.

    Article  Google Scholar 

  5. Kato, T. 1993. Abstract evolution equation linear and quasilinear, revisited. Lecture Notes in Mathematics 1540: 103–125.

    Article  MathSciNet  MATH  Google Scholar 

  6. Oka, H., and N. Tanaka. 1997. Abstract quasilinear integrodifferential equations of hyperbolic type. Nonlinear Analysis 29: 903–925.

    Article  MathSciNet  MATH  Google Scholar 

  7. Pazy, A. 1983. Semigroups of Linear Operators and Applications to Partial Differential Equations. New York: Springer.

    Book  MATH  Google Scholar 

  8. Luo, Z., and J. Shen. 2001. Stability results for impulsive functional differential equations with infinite delays. Journal of Computational and Applied Mathematics 131: 55–64.

    Article  MathSciNet  MATH  Google Scholar 

  9. Luo, Z., and J. Shen. 2003. Impulsive stabilization of Functional differential equations with infinite delays. Applied Mathematics Letters 16: 695–701.

    Article  MathSciNet  MATH  Google Scholar 

  10. Luo, Z., and J. Shen. 2009. Stability of impulsive functional differential equations via the Liapunov functional. Applied Mathematics Letters 22: 163–169.

    Article  MathSciNet  Google Scholar 

  11. Radhakrishnan, B. 2015. Existence of Quasilinear neutral impulsive integrodifferential equations in Banach space. International Journal of Analysis and Applications 7: 22–37.

    MATH  Google Scholar 

  12. Radhakrishnan, B. 2017. Existence of Solutions for Semilinear Neutral Impulsive Mixed Integrodifferential Inclusions of Sobolev Type in Banac Spaces. Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis 24: 317–332.

    MathSciNet  MATH  Google Scholar 

  13. Radhakrishnan, B., and M. Tamilarasi. 2018. Existence of solutions for quasilinear random impulsive neutral differential evolution equation. Arab Journal of Mathematical Sciences 24: 235–246.

    Article  MathSciNet  MATH  Google Scholar 

  14. Rogovchenko, Yu.V. 1997. Impusive evolution systems: main results and new trends. Dynamics of Continuous, Discrete and Impulsive Systems 3: 57–88.

    MathSciNet  MATH  Google Scholar 

  15. Samoilenko, A.M., and N.A. Perestyuk. 1995. Impulsive Differential Equations. Singapore: World Scientific.

    Book  MATH  Google Scholar 

  16. Sathiyaraj, T., and P. Balasubramaniam. 2016. Controllability of fractional neutral stochastic integrodifferential inclusions of order \(p \in (0, 1], q \in (1, 2]\) with fractional Brownian motion. The European Physical Journal Plus 131: 357.

    Article  Google Scholar 

  17. Sathiyaraj, T., and P. Balasubramaniam. 2016. Controllability of Fractional Order Stochastic Differential Inclusions with Fractional Brownian Motion in Finite Dimensional Space. IEEE/CAA Journal of Automatica Sinica 4: 400–410.

    MathSciNet  Google Scholar 

  18. Vinodkumar, A. 2011. Existence results on random impulsive semilinear functional differential inclusions with delays. Annals of Functional Analysis 3: 89–106.

    Article  MathSciNet  MATH  Google Scholar 

  19. Vinodkumar, A., and A. Anguraj. 2011. Existence of random impulsive abstract neutral non-autonomous differential inclusions with delay. Nonlinear Analysis-Hybrid system 5: 413–426.

    Article  MathSciNet  MATH  Google Scholar 

  20. Wu, S.J., and X.Z. Meng. 2004. Boundedness of nonlinear differential systems with impulsive effect on random moments. Acta Mathematicae Applicatae Sinica 20: 147–154.

    Article  MathSciNet  MATH  Google Scholar 

  21. Wu, S.J., and D. Han. 2005. Exponential stability of functional differential systems with impulsive effect on Random Moments. Computers and Mathematics with Applications 50: 321–328.

    Article  MathSciNet  MATH  Google Scholar 

  22. Wu, S.J., X.L. Guo, and Y. Zhou. 2006. p-moment stability of functional differential equations with random impulses. Computational Mathematics with Applications 52: 1683–1694.

    Article  MathSciNet  MATH  Google Scholar 

  23. Wu, S.J., X. Guo, and Z.S. Lin. 2006. Existence and uniqueness of solutions to random impulsive differential systems. Acta Mathematicae Applicatae Sinica 4: 627–632.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors sincerely thank the anonymous reviewer for his careful reading, constructive comments and fruitful suggestions to improve the quality of the paper.

Author information

Authors and Affiliations

  1. Department of Mathematics, PSG College of Technology, Coimbatore, 641004, India

    B. Radhakrishnan & M. Tamilarasi

Authors
  1. B. Radhakrishnan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Tamilarasi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. Radhakrishnan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Radhakrishnan, B., Tamilarasi, M. Existence results for quasilinear random impulsive abstract differential inclusions in Hilbert space. J Anal 27, 327–345 (2019). https://doi.org/10.1007/s41478-018-0132-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41478-018-0132-3

Keywords

Mathematics Subject Classification

Search

Navigation