A linear periodic boundary-value problem for a second-order hyperbolic equation - Khoma, N. H.; Khoma, L. G. (Ukrains’kyi Matematychnyi Zhurnal, 1999)
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 \(\frac{π }{q} - , \frac{{2π }}{{2s - 1}} - \) , and \(\frac{{4π }}{{2s - 1}}\) -periodic functions (q and s are natural numbers). We obtain the results only for sets of periods \(T_1 = (2p - 1)\frac{π }{q}, T_2 = (2p - 1)\frac{{2π }}{{2s - 1}}\) , and \(T_3 = (2p - 1)\frac{{4π }}{{2s - 1}}\) which characterize the classes of π-, 2π -, and 4π-periodic functions.