Skip to main content
SpringerLink
Log in

An existence principle for a periodic solution of a differential equation in Banach space

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

Abstract

The equation d2x/dt2=Ax +f(t, x) is considered in a Banach space E, where A is a fixed unbounded linear operator, andf(t, x) is a nonlinear operator which is periodic in t and satisfies a Lipschitz condition with respect to x ε E. Existence conditions have been obtained for a well defined generalized periodic solution of this equation, and also when this solution coincides with the true solution. Similar results have been obtained for the first order equation.

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

Literature cited

  1. P. E. Sobolevskii, “Equations of parabolic type in Banach space,” Tr. Mosk. Matem. Ob-va,10, 297–350 (1961).

    Google Scholar 

  2. M. A. Krasnosel'skii, Displacement Operators along Trajectories of Differential Equations [in Russian], Moscow (1966).

  3. I. I. Shmulev, “Periodic solutions of the first boundary problem for parabolic equations,” Matem. Sb.,66, No. 3, 398–410 (1965).

    Google Scholar 

  4. D. Tsend, “An existence theorem for a periodic solution of a nonlinear parabolic equation,” Vestnik Mosk. Un-ta, No. 3, 32–36 (1967).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Vladimir Pedogogical Institute, USSR

    N. V. Medvedev

Authors
  1. N. V. Medvedev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskie Zametki, Vol. 4, No. 1, pp. 105–112, July, 1968.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Medvedev, N.V. An existence principle for a periodic solution of a differential equation in Banach space. Mathematical Notes of the Academy of Sciences of the USSR 4, 551–554 (1968). https://doi.org/10.1007/BF01429820

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01429820

Keywords

Search

Navigation