Problem for hyperbolic system of equations having constant coefficients with integral conditions with respect to the time variable

Abstract

In a domain specified in the form of a Cartesian product of a segment $\left[0,T\right]$ and the space ${\mathbb R}^{p}$, we study a problem with integral conditions with respect to the time variable for  hyperbolic system with constant coefficients in a class of almost periodic functions in the space variables. A criterion for the unique solvability of this problem and sufficient conditions for the existence of its solution are established. To solve the problem of small denominators arising in the construction of solutions of the posed problem, we use the metric approach.