Skip to main content
SpringerLink
Log in

Some uniqueness results for functional damped semilinear differential equations in Fréchet spaces

  • Published:
Acta Mathematica Sinica, English Series Aims and scope Submit manuscript

Abstract

A recent nonlinear alternative for contraction maps in Fréchet spaces due to Frigon and Granas (Résultats de type Leray-Schauder pour des contractions sur des espaces de Fréchet, Ann. Sci. Math. Québec 22, (2), 161–168 (1998)), combined with semigroup theory, is used to investigate the existence and uniqueness of mild solutions for first-and second-order functional semi linear and neutral damped differential equations in Fréchet space.

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. Frigon, M., Granas, A.: Résultats de type Leray-Schauder pour des contractions sur des espaces de Fréchet. Ann. Sci. Math. Québec, 22(2), 161–168 (1998)

    MATH  MathSciNet  Google Scholar 

  2. Bélair, J.: Poulation modales with state-depending delays, in Mathematical Population Dynamic (O. Arino, D. Axelrod, and M. Kimmel, Eds.). Lecture Notes in Pure and Appl. Math. Dekker, New York, 131, 165–177 (1991)

  3. Erbe, L. H., Kong, Q., Zhang, B. G.: Oscillation Theory for Functional Differential Equations, Pure and Applied Mathematics, Marcel Dekker, New York, 1994

    Google Scholar 

  4. Hale, J. K.: Theory of Functional Differential Equations, Springer, New York, 1977

    MATH  Google Scholar 

  5. Henderson, J.: Boundary Value Problems for Functional Differential Equations, World Scientific, Singapore, 1995

    MATH  Google Scholar 

  6. Patcheu, S. K.: On the global solution and asymptotic behaviour for the generalized damped extensible beam equation. J. Differential Equations, 135, 299–314 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  7. Matos, M., Pereira, D.: On a hyperbolic equation with strong damping. Funkcial. Ekvac., 34, 303–311 (1991)

    MATH  MathSciNet  Google Scholar 

  8. Pazy, A.: Semigroups of linear operators and applications to partial differential equation, Springer-Verlag, New York, 1983

    Google Scholar 

  9. Goldstein, J. A.: Semigroups of Linear Operators and Applications, Oxford, New York, 1985

    MATH  Google Scholar 

  10. Hernandez, E., Mckibben, M. A.: Some comments on existence of solutions of abstract nonlinear second-order neutral functional integrodifferential equations. Comput. Math. Appl., 50, 655–669 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  11. Xue, X. M.: Existence of semilinear differential equations with nonlocal initial conditions. Acta Mathematica Sinica, English Series, 23, 983–988 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  12. Benchohra, M., Ntouyas, S. K.: Existence of mild solutions on semiinfinite intervals for first order differential equations with nonlocal conditions. Comment. Math. Univ. Carol., 41, 485–491 (2000)

    MATH  MathSciNet  Google Scholar 

  13. Agarwal, R. P., O’Regan, D.: Infinite Interval Problems for Differential, Difference and Integral Equations, Kluwer Acad. Pub., Dordrecht, 2001

    MATH  Google Scholar 

  14. Ouahab, A.: Local and global existence and uniqueness results for impulsive differential equations with multiple delay. J. Math. Anal. Appl., 323, 456–472 (2006)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  17. Fattorini, H. O.: Second Order Linear Differential Equations in Banach Spaces, North-Holland, Mathematical Studies Vol. 108, North-Holland, Amsterdam, 1985

    MATH  Google Scholar 

  18. Travis, C. C., Webb, G. F.: Second order differential equations in Banach spaces, Proc. Int. Symp. on Nonlinear Equations in Abstract Spaces, Academic Press, New York, 1978, 331–361

    Google Scholar 

  19. Travis, C. C., Webb, G. F.: Cosine families and abstract nonlinear second order differential equations. Acta Math. Hung., 32, 75–96 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  20. Engel, K. J., Nagel, R.: One-Parameter Semigroups for Linear Evolution Equations, Springer-Verlag, New York, 2000

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Mathématiques, Université de Sidi Bel Abbès, BP 89, 22000, Sidi Bel Abbès, Algérie

    Abdelghani Ouahab

Authors
  1. Abdelghani Ouahab
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abdelghani Ouahab.

Additional information

Supported by laboratory of mathematics of Sidi Bel Abbes

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ouahab, A. Some uniqueness results for functional damped semilinear differential equations in Fréchet spaces. Acta. Math. Sin.-English Ser. 24, 95–106 (2008). https://doi.org/10.1007/s10114-007-0999-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-007-0999-4

Keywords

MR(2000) Subject Classification

Search

Navigation