Skip to main content
Log in

Cauchy problem for a differential equation in the Banach space with generalized strongly positive operator coefficient

  • Published:
Ukrainian Mathematical Journal Aims and scope

The concept of strongly positive operator is generalized and the properties of the introduced operators are analyzed. The solutions of the Cauchy problem for a linear inhomogeneous differential equation with generalized strongly positive operator coefficient are obtained.

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.

Institutional subscriptions

Similar content being viewed by others

References

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

    MATH  Google Scholar 

  2. S. G. Krein, Linear Differential Equations in Banach Space, Amer. Math. Soc., Providence, RI (1971).

  3. E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups, Amer. Mat. Soc., Providence, RI (1957).

  4. T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin (1995).

    MATH  Google Scholar 

  5. V. L. Makarov and I. P. Gavrilyuk, “Exponentially convergent methods for the parallel discretization of the first-order evolution equations,” Dop. Nats. Akad. Nauk Ukr., No. 3, 24–28 (2002).

  6. I. P. Gavrilyuk, W. Hackbusch, and B. N. Khoromskij, “Data-sparse approximation to the operator-valued functions of elliptic operator,” Math. Comput., 73, No. 247, 1297–1324 (2004).

    MathSciNet  MATH  Google Scholar 

  7. D. Henry, Geometric Theory of Semilinear Parabolic Equations, Springer, Berlin (1981).

    MATH  Google Scholar 

  8. M. F. Gorodnii and A. V. Chaikovskii, “Generalization of the notion of sectorial operator,” Mat. Sb., 197, No. 7, 29–46 (2006).

    MathSciNet  Google Scholar 

  9. I. P. Gavrilyuk and V. L. Makarov, Strongly Positive Operators and Algorithms without Accuracy Saturation [in Russian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev (2004).

    Google Scholar 

  10. A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis, Dover, New York (1999).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 8, pp. 1053–1070, August, 2011.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Il’chenko, Y.V., Chaikovs’kyi, A.V. Cauchy problem for a differential equation in the Banach space with generalized strongly positive operator coefficient. Ukr Math J 63, 1213–1233 (2012). https://doi.org/10.1007/s11253-012-0573-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-012-0573-9

Keywords

Navigation