Skip to main content
SpringerLink
Log in

Estimates of the volume of solutions of differential equations with Hukuhara derivative

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

For a class of nonlinear differential equations with Hukuhara derivative, lower bounds for the volume of their solutions are obtained. A. D. Aleksandrov’s classical inequalities for mixed volumes combined with the comparison method are used.

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. L. Stefanini and B. Bede, “Generalized Hukuhara differentiability of the interval-valued functions and interval differential equations,” Nonlinear Anal. 71 (3–4), 1311–1328 (2009).

    Article  MATH  MathSciNet  Google Scholar 

  2. B. Bede and L. Stefanini, “Solution of fuzzy differential equations with generalized differentiability using LU-parametric representation,” in Proceedings of the 7th Conference of the European Society for Fuzzy Logic and Technology and 17th Annual LFA Meeting (Atlantis Press, Amsterdam, 2011), pp. 785–790.

    Google Scholar 

  3. A. A. Tolstonogov, Differential Inclusions in a Banach Space (Nauka, Novosibirsk, 1986) [in Russian].

    MATH  Google Scholar 

  4. V. Lakshmikantham, T. G. Bhaskar, and J. V. Devi, Theory of Set Differential Equations in Metric Spaces (Cambridge Sci. Publ., Cambridge, 2006).

    MATH  Google Scholar 

  5. A. D. Aleksandrov, “To the theory of mixed volumes of convex bodies. IV. Mixed discriminants and mixed volumes,” Mat. Sb. 3 (2), 227–251 (1938).

    Google Scholar 

  6. A. D. Aleksandrov, “To the theory ofmixed volumes of convex bodies. I. Extension of some notions of the theory of convex bodies,” Mat. Sb. 2 (5), 947–972 (1937).

    Google Scholar 

  7. A. D. Aleksandrov, “To the theory of mixed volumes of convex bodies. II. New inequalities between mixed volumes and their applications,” Mat. Sb. 2 (6), 1205–1238 (1937).

    Google Scholar 

  8. A. D. Aleksandrov, “To the theory of mixed volumes of convex bodies. III. Extension of two Minkowski theorems on convex polyhedra to arbitrary convex bodies,” Mat. Sb. 3 (1), 27–46 (1938).

    Google Scholar 

  9. N. Rouche, P. Habets, and M. Laloy, Stability Theory by Lyapunov’s Direct Method (Springer-Verlag, New York, 1980; Mir, Moscow, 1980).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Cherkasy State Technological University, Cherkasy, Ukraine

    E. V. Ocheretnyuk

  2. Timoshenko Institute of Mechanics, National Academy of Sciences, Kiev, Ukraine

    V. I. Slyn’ko

Authors
  1. E. V. Ocheretnyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. I. Slyn’ko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. V. Ocheretnyuk.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ocheretnyuk, E.V., Slyn’ko, V.I. Estimates of the volume of solutions of differential equations with Hukuhara derivative. Math Notes 97, 431–437 (2015). https://doi.org/10.1134/S0001434615030141

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001434615030141

Keywords

Search

Navigation