Skip to main content
Log in

Some Uniqueness Results on Controllability for Functional Semilinear Differential Equations in Fréchet Spaces

  • Published:
Nonlinear Oscillations

Abstract

In this paper, a recent nonlinear alternative for contraction maps in Fréchet spaces, due to Frigon and Granas, is combined with semigroup theory and used for the investigation of the controllability of some classes of semilinear functional and neutral functional differential equations in Banach spaces on a semiinfinite interval.

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. M. Frigon and A. Granas, “Résultats de type Leray—Schauder pour des contractions sur des espaces de Férchet,” Ann. Sci. Math. Québec, 22, No. 2, 161–168 (1998).

    Google Scholar 

  2. K. Balachandran and J. P. Dauer, “Controllability of nonlinear systems in Banach spaces. A survey,” J. Optimiz. Theory Appl., 115, 7–28 (2002).

    Google Scholar 

  3. M. Benchohra and S. K. Ntouyas, “Controllability on infinite time horizon of nonlinear differential equations in Banach spaces with nonlinear conditions,” An. Şti. Univ. Iaşi. Mat. (N.S.), 47, 277–286 (2001).

    Google Scholar 

  4. K. Yosida, Functional Analysis, Springer, Berlin (1980).

    Google Scholar 

  5. H. O. Fattorini, Second-Order Linear Differential Equations in Banach Spaces, North-Holland, Amsterdam (1985).

  6. J. A. Goldstein, Semigroups of Linear Operators and Applications, Oxford University Press, New York (1985).

    Google Scholar 

  7. C. C. Travis and G. F. Webb, “Second-order differential equations in Banach spaces,” Proceedings of the International Symposium on Nonlinear Equations in Abstract Spaces, Academic Press, New York (1978), pp. 331–361.

    Google Scholar 

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

    Google Scholar 

  9. K. J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Springer, New York (2000).

    Google Scholar 

  10. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York (1983).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Arara, A., Benchohra, M. & Ouahab, A. Some Uniqueness Results on Controllability for Functional Semilinear Differential Equations in Fréchet Spaces. Nonlinear Oscillations 6, 287–303 (2003). https://doi.org/10.1023/B:NONO.0000016408.46234.48

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:NONO.0000016408.46234.48

Keywords

Navigation