On the periodic solutions of the second-order wave equations. V

• Date: 1993
• Main Authors: Mitropolskiy, Yu. A., Khoma, G. P., Митропольський, Ю. О., Хома, Г. П.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 1993
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5908
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

It is established that the linear problem $u_{tt} - a^2 u_{xx} = g(x, t),\quad u(0, t) = u(\pi, t),\quad u(x, t + T) = u(x, t)$ is always solvable in the space of functions $A = \{g:\; g(x, t) = g(x, t + T) = g(\pi - x, t) = -g(-x, t)\}$ provided that $aTq = (2p - 1)\pi, \quad (2p - 1, q) = 1$, wher...