Existence and uniqueness results for mild solutions of random impulsive abstract neutral partial differential equation over real axis

Article
  • 47 Downloads

Abstract

In this paper, we discuss the existence and uniqueness of mild solutions of random impulsive abstract neutral partial differential equations in a real separable Hilbert space. The results are obtained by using Leray-Schauder Alternative and Banach Contraction Principle. Finally an example is given to illustrate our problem.

Keywords

neutral equation Leray Schauder Alternative Banach Contraction Principle semigroup of linear operators 

MR Subject Classification

34K40 34A37 35A01 35A02 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

The authors sincerely thank the reviewers for their careful reading, comments and suggestions to improve the quality of the manuscript.

References

  1. [1]
    S Dhanalakshmi, R Murugesu, R Poongodi. Global existence for impulsive abstract partial neutral functional volterra-fredholm integrodifferential equations, Internat J Math Arch, 2013, 4: 214–230.Google Scholar
  2. [2]
    E Hernández Morales, MA Mckibben, HR Henríquez. Existence results for partial neutral functional differential equations with state-dependent delay, Math Comput Modelling, 2009, 49: 1260–1267.MathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    E Hernández. Global solutions for abstract neutral differential equations, Nonlinear Anal, 2010, 72: 2210–2218.MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    E Hernández. Global Solutions for abstract impulsive neutral differential equations, Math Comput Modelling, 2011, 53: 196–204.MathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    E Hernández, HR Hernráquez. Existence results for partial neutral functional differential equation with unbounded delay, J Math Anal Appl, 1998, 221: 452–475.MathSciNetCrossRefGoogle Scholar
  6. [6]
    E Hernández, M Pierri, G Gonclaves. Existence results for an impulsive partial differential equation with state-dependent delay, Comput Math Appl, 2006, 52: 411–420.MathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    E Hernández, D O’Regan. Existence results for abstract partial neutral differential equations, Proc Amer Math Soc, 2009, 137: 3309–3318.MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    F Jiang, H Yang, Y Shen. A note on exponential stability for second-order neutral stochastic partial differential equations with infinite delays in the presence of impulses, Appl Math Comput, 2016, 287: 125–133.MathSciNetGoogle Scholar
  9. [9]
    A Granas, J Dugundji. Fixed Point Theory, Springer-Verlag, New York, 2003.CrossRefMATHGoogle Scholar
  10. [10]
    H Yang, JG Liu, F Jiang. Exponential stability of jump-diffusion systems with neutral term and impulses, Math Probl Eng, 2015, Volume 2015, Article ID 192083, 7 pages.Google Scholar
  11. [11]
    Y Hino, S Murakami, T Naito. Functional-Differential Equations with Infinite Delay, Lecture notes in Math, Vol 1473, 1991.Google Scholar
  12. [12]
    V Lakshmikantham, DD Bainov, PS Simeonov. Theory of Impulsive Differential Equations, Series in Modern Applied Mathematics, Vol 6, World Scientific, Singapore, 1989.Google Scholar
  13. [13]
    A Lunardi. Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhauser, Berlin, 1995.CrossRefMATHGoogle Scholar
  14. [14]
    MM Arjunan, V kavitha. Existence results for impulsive neutral functional differential equations with state-dependent delay, Electron J Qual Theory Differ Equ, 2009, 26: 1–13.MathSciNetCrossRefMATHGoogle Scholar
  15. [15]
    AM Samoilenko, NA Prestyuk. Impulsive Differential Equations, World Scientific, Singapore, 1995.CrossRefGoogle Scholar
  16. [16]
    SJ Wu, XZ Meng. Boundedness of nonlinear differential systems with impulsive effect on random moments, Acta Math Appl Sin, 2004, 20: 147–154.MathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    YK Chang, ZH Zhao, JJ Nieto. Global existence results for a stochastic differential equations in hilbert spaces, Fixed Point Theory, 2012, 13: 35–48.MathSciNetMATHGoogle Scholar

Copyright information

© Editorial Committee of Applied Mathematics-A Journal of Chinese Universities and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsTamilnadu College of EngineeringCoimbatoreIndia
  2. 2.Department of MathematicsAnna University Regional CentreCoimbatoreIndia

Personalised recommendations