Skip to main content
SpringerLink
Log in

On trivial differential equations in the spaces Lp, 0<p<1

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

A description of the set Xp of all solutions of the trivial Cauchy problem in Lp, o< p<1, is presented. The principal result is Theorem 2, which asserts that Xp is a closed subspace of the p-Banach space Hp of all curves in Lp that satisfy a Hölder condition of order p and emanate from O relative to the p-norm, which is equal to the minimal constant in the Hölder condition.

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. S. Rolewicz, Metric Linear Spaces, PWN, Warsaw (1985), 458 pp.

    Google Scholar 

  2. S. Rolewicz, “On fonctions with zero derivative,” Wiad. Mat.,3, 127–128 (1959).

    Google Scholar 

  3. S. Rolewicz, Metric Linear Spaces, PWN, Warsaw (1972), 287 pp.

    Google Scholar 

  4. N. J. Kalton, “Curves with zero derivatives in F-spaces,” Glasgow Math. J.,22, 19–29 (1981).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Zaporizhzhia University, USSR

    L. V. Popova

Authors
  1. L. V. Popova
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrayins'kyy Matematychnyy Zhurnal, Vol. 44, No. 9, pp. 1238–1242, September, 1992.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Popova, L.V. On trivial differential equations in the spaces Lp, 0<p<1. Ukr Math J 44, 1132–1135 (1992). https://doi.org/10.1007/BF01058375

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01058375

Keywords

Search

Navigation