Skip to main content

Existence and Uniqueness Results for Impulsive Functional Integro-Differential Inclusions with Infinite Delay

  • Conference paper
Control, Computation and Information Systems (ICLICC 2011)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 140))

  • 1158 Accesses

Abstract

In this paper, we discuss the existence of mild solutions of first-order impulsive functional integro-differential inclusions with scalar multiple delay and infinite delay. The result is obtained by using a fixed point theorem for condensing maps due to Martelli.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bainov, D.D., Simeonov, P.S.: Systems with Impulsive Effect. Horwood, Chichester (1989)

    MATH  Google Scholar 

  2. Benchohra, M., Henderson, J., Ntouyas, S.K., Ouahab, A.: Boundary value problems for impulsive functional differential equations with infinite delay. International Jour. Math. Comput. Sci. 1, 27–39 (2006)

    MathSciNet  MATH  Google Scholar 

  3. Chang, Y.K., Nieto, J.J.: Existence of solutions for impulsive neutral integro-differential inclusions with nonlocal initial conditions via fractional operators. Numer. Funct. Anal. Optim. 30, 227–244 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Laksmikantham, V., Bainov, D.D., Simeonov, P.S.: Theory of Impulsive Differential Equations. World Scientific, Singapora (1989)

    Book  Google Scholar 

  5. Lasota, A., Opial, Z.: An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations. Bull. Acad. Pol. Sci. Ser. Sci. Math. Astronorm. Phys. 13, 781–786 (1965)

    MathSciNet  MATH  Google Scholar 

  6. Lin, A., Hu, L.: Existence results for impulsive neutral stochastic functional integro-differential inclusions with nonlocal initial conditions. Comp. Math. Appl. 59, 64–73 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. Luo, Z., Nieto, J.J.: New results for the periodic boundary value problem for impulsive integro-differential equations. Nonlinear Anal. 70, 2248–2260 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Martelli, M.A.: A Rothe’s type theorem for noncompact acyclic-valued maps. Bollettino della Unione Mathematica Italiana 4, 70–76 (1975)

    MathSciNet  MATH  Google Scholar 

  9. Nieto, J.J., Rodríguez-López, R.: New comparison results for impulsive integro-differential equations and applications. J. Math. Anal. Appl. 328, 1343–1368 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ouahab, A.: Existence and uniqueness results for impulsive functional differential equations with scalar multiple delay and infinite delay. Nonlinear Anal. 67, 1027–1041 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  11. Samoilenko, A.M., Perestyuk, N.A.: Impulsive Differential Euqations. World Scientific, Singapore (1995)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Park, J.Y., Jeong, J.U. (2011). Existence and Uniqueness Results for Impulsive Functional Integro-Differential Inclusions with Infinite Delay. In: Balasubramaniam, P. (eds) Control, Computation and Information Systems. ICLICC 2011. Communications in Computer and Information Science, vol 140. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19263-0_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-19263-0_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-19262-3

  • Online ISBN: 978-3-642-19263-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics