Existence of a countable set of periodic solutions of the problem of forced oscillations for a weakly nonlinear wave equation

In the strip $0<x<\pi$ of the plane of the points $t$, $x$ the following boundary value problem is considered:
\begin{gather*} u_{tt}-u_{xx}=\pm|u|^{p-2}u+h(t,x)\quad(0<x<\pi),\qquad u(t,0)=u(t,\pi)=0, \\ u(t+2\pi,x)=u(t,x). \end{gather*}
It is proved that for any $p>2$ and for an arbitrary $2\pi$-periodic function $h$ which is locally integrable with power $p(p-1)^{-1}$ this problem has a countable set of geometrically distinct generalized solutions.
Bibliography: 15 titles.