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Ukrainian Mathematical Journal

, Volume 51, Issue 11, pp 1779–1781 | Cite as

On a smooth solution of a nonlinear periodic boundary-value problem

  • I. V. Dombrovskii
Brief Communications
  • 12 Downloads

Abstract

We establish conditions for the existence of a smooth solution of a quasilinear hyperbolic equationu tt - uxx = ƒ(x, t, u, u, u x),u (0,t) = u (π,t) = 0,u (x, t+ T) = u (x, t), (x, t) ∈ [0, π] ×R, and prove a theorem on the existence and uniqueness of a solution.

Keywords

Banach Space Wave Equation Periodic Solution Integral Representation Russian Translation 
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

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    L. G. Khoma and N. G. Khoma, “A linear boundary-value problem for a second-order hyperbolic equation,”Ukr. Mat. Zh.,51, No. 2, 281–284 (1999).zbMATHCrossRefMathSciNetGoogle Scholar
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    O. Vejvoda and M. Štedry, “Existence of classical periodic solutions for wave equations: the relationship between the number-theoretical character of the period and the geometrical properties of solutions,”Differents. Uravn.,20, No. 10, 1733–1739 (1984).Google Scholar
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    P. Hartman,Ordinary Differential Equations [Russian translation], Mir, Moscow (1970).zbMATHGoogle Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 2000

Authors and Affiliations

  • I. V. Dombrovskii
    • 1
  1. 1.Ternopol Pedagogical UniversityTernopol

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