Almost periodic solutions of one dimensional wave equations with periodic coefficients (Q810733)

The author establishes conditions under which all solutions of an initial-boundary value problem for the equation \[ u_{xx}- u_{tt}+\epsilon (p(t)u+q(t)u_ t)=f(x,t),\quad x\in (0,\pi), \] are almost periodic, where \(\epsilon\) is a small parameter, p(t) and q(t) are periodic with period \(2\pi\) /\(\omega\) and f is almost periodic. The paper mainly deals with the case where the ratio \(2\pi\) /\(\omega\) is irrational and \(\int^{2\pi /\omega}_{0}q(t) dt=0\).