Skip to main content
Log in

Controllability of impulsive functional differential inclusions with infinite delay in Banach spaces

  • Published:
Journal of Applied Mathematics and Computing Aims and scope Submit manuscript

Abstract

In this paper, we establish a sufficient condition for the controllability of the first-order impulsive functional differential inclusions with infinite delay in Banach spaces. The approach used is the nonlinear alternative of Leray-Schauder type for multivalued maps. An example is also given to illustrate our result.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. K. Balachandran and J. P. Dauer,Controllability of nonlinear systems in Banach spaces: a survey, J. Optim. Theory Appl.115 (2002), 7–28.

    Article  MATH  MathSciNet  Google Scholar 

  2. K. Balachandran and E. R. Anandhi,Controllability of neutral functional integrodifferential infinite delay systems in Banach spaces, Taiwanese J. Math.8 (2004) 689–702.

    MATH  MathSciNet  Google Scholar 

  3. M. Benchohra, L. Górniewicz, S. K. Ntouyas and A. Ouahab,Controllability results for impulsive functional differential inclusions, Rep. Math. Phys.54(2) (2004), 211–228.

    Article  MATH  MathSciNet  Google Scholar 

  4. K. Deimling,Multivalued Differential Equations, De Gruyter, Berlin, 1992.

    MATH  Google Scholar 

  5. J. Dugundij and A. Grans,Fixed point theory, Mongrafie Mat. PWN, Warsaw, 1982.

    Google Scholar 

  6. C. Gao, Y. Lang, E. Feng and Z. Xiu,Nonlinear impulsive system of microbial production in fed-batch culture and its optimal control, J. Appl. Math. & Computing19 (2005), 203–214.

    MATH  MathSciNet  Google Scholar 

  7. X. Fu,Controllability of abstract neutral functional differential systems with unbounded delay, Appl. Math. Comp.151 (2004), 299–314.

    Article  MATH  Google Scholar 

  8. H. K. Han, J. Y. Park and D. G. Park,Controllability of integrodifferential equations in Banach spaces, Bull. Korean Math. Soc.36 (1999), 533–541.

    MATH  MathSciNet  Google Scholar 

  9. E. Hernandez and H. R. Henriquez,Existence results for partial neutral functional differential equations with unbounded delay, J. Math. Anal. Appl.221 (1998), 452–475.

    Article  MATH  MathSciNet  Google Scholar 

  10. S. Hu and N. Papageorgiou,Handbook of multivalued analysis, Kluwer, Dordrecht, Boston, 1997.

    MATH  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  12. Y. Liu, J. Xia and W. Ge,Positive periodic solutions of impulsive functional differential equations, J. Appl. Math. & Computing19 (2005), 261 - 280.

    Article  MATH  MathSciNet  Google Scholar 

  13. J. R. Kang, Y. C. Kwun and J. Y. Park,Controllability of the second-order differential inclusion in Banach spaces, J. Math. Anal. Appl.285 (2003), 537–550.

    Article  MATH  MathSciNet  Google Scholar 

  14. J. Y. Park, Y. C. Kwun and H. J. Lee,Controllability of second-order neutral functional differential inclusions in Banach Spaces, J. Math. Anal. Appl.258 (2003), 37–49.

    Article  MathSciNet  Google Scholar 

  15. A. Pazy,Semigroups of Linear Operators and Applications to Partial Equations, in: Applied Mathematical Sciences, Vol. 44, Springer Verlag, New York, NY, 1983.

    Google Scholar 

  16. M. D. Quinn and N. Carmichael,An approach to nonlinear control problem using fixed point methods, degree theory and pseudo-inverses, Numer. Funct. Anal. Optim.23 (1991), 109–154

    Google Scholar 

  17. J. H. Wu,Theory and Applications of Partial Functional Differential Equations, in: Applied Mathematical Sciences, Vol. 119, Springer Verlag, New York, NY, 1996.

    Google Scholar 

  18. B. Yan,Boundary value problems on the half-line with impulses and infinite delay, J. Math. Anal. Appl.259 (2001), 94–114.

    Article  MATH  MathSciNet  Google Scholar 

  19. K. Yosida,Functional Analysis, 6th edn. Springer-Verlag, Berlin, 1980.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yong-Kui Chang.

Additional information

Supported by “Qing Lan” Talent Engineering Funds (QL-05-164) by Lanzhou Jiaotong University.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chang, YK. Controllability of impulsive functional differential inclusions with infinite delay in Banach spaces. J. Appl. Math. Comput. 25, 137–154 (2007). https://doi.org/10.1007/BF02832343

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02832343

AMS Mathematics Subject Classification

Key words and phrases

Navigation