Ukrainian Mathematical Journal

, Volume 51, Issue 2, pp 319–323 | Cite as

A linear periodic boundary-value problem for a second-order hyperbolic equation

  • L. G. Khoma
  • N. G. Khoma
Brief Communications


We study the boundary-value problemu tt -u xx =g(x, t),u(0,t) =u (π,t) = 0,u(x, t +T) =u(x, t), 0 ≤x ≤ π,t ∈ ℝ. We findexact classical solutions of this problem in three Vejvoda-Shtedry spaces, namely, in the classes of\(\frac{\pi }{q} - , \frac{{2\pi }}{{2s - 1}} - \), and\(\frac{{4\pi }}{{2s - 1}}\)-periodic functions (q and s are natural numbers). We obtain the results only for sets of periods\(T_1 = (2p - 1)\frac{\pi }{q}, T_2 = (2p - 1)\frac{{2\pi }}{{2s - 1}}\), and\(T_3 = (2p - 1)\frac{{4\pi }}{{2s - 1}}\) which characterize the classes of π-, 2π -, and 4π-periodic functions.


Periodic Solution Natural Number Classical Solution Naukova Dumka Unique Function 
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Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • L. G. Khoma
    • 1
  • N. G. Khoma
    • 2
  1. 1.Ternopol Pedagogical University TernopolUkraine
  2. 2.Ternopol Academy for AgricultureTernopol

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