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 \(π q - , 2π 2s - 1 - \) , and \(4π 2s - 1 \) -periodic functions (q and s are natural numbers). We obtain the results only for sets of periods \(T_1 = (2p - 1)π q, T_2 = (2p - 1)2π 2s - 1 \) , and \(T_3 = (2p - 1)4π 2s - 1 \) which characterize the classes of π-, 2π -, and 4π-periodic functions.