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Ukrainian Mathematical Journal

, Volume 49, Issue 12, pp 1907–1911 | Cite as

Quasilinear periodic boundary-value problem

  • A. G. Botyuk
Brief Communications

Abstract

We study a periodie boundary-value problem for the quasilinear equation u tt u xx = F[u, u t , u x ]. We find conditions under which a theorem on the uniqueness of a solution is true.

Keywords

Differential Equation Banach Space Integral Equation Unique Solution Ordinary Differential Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Yu. A. Mitropol’skii, G. P. Khoma, and M. I. Gromyak. Asymptotic Methods for the Investigation of Quasilinear Hyperbolie Equations [in Russian], Naukova Dumka, Kiev (1991).Google Scholar
  2. 2.
    L. H. Khoma, N. H. Khoma, and A. O. Botyuk, “The existence of the Vejvoda-Shtedry spaces,” Ukr. Mat. Zh., 49, No. 2, 302–308 (1997).CrossRefMathSciNetGoogle Scholar
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    P. Hartman, Ordinary Differential Equations, John Wiley & Sons, New York (1964).zbMATHGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • A. G. Botyuk

There are no affiliations available

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