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


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.


Banach Space Wave Equation Periodic Solution Integral Representation Russian Translation 
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Copyright information

© Kluwer Academic/Plenum Publishers 2000

Authors and Affiliations

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

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