2017
Том 69
№ 7

Всі номери

О периодических решениях волновых уравнений второго порядка

Митропольський Ю. О., Хома Г. П.

Повний текст (.pdf)


Абстракт

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 $aTq = (2p - 1)\pi, \quad (2p - 1, q) = 1$, where $p, q$ are integers. To prove this statement, an explicit solution is constructed in the form of an integral operator which is used to prove the existence of a solution to aperiodic boundary value problem for nonlinear second order wave equation. The results obtained can be employed in the study of solutions to nonlinear boundary value problems by asymptotic methods.

Англомовна версія (Springer): Ukrainian Mathematical Journal 45 (1993), no. 8, pp 1244-1251.

Зразок цитування: Митропольський Ю. О., Хома Г. П. О периодических решениях волновых уравнений второго порядка // Укр. мат. журн. - 1993. - 45, № 8. - С. 1115–1121.

Повний текст