In a domain obtained as a Cartesian product of an interval $[0, T]$ and the space $R^p, p \in N$, for a system of equations (with
constant coefficients) unsolved with respect to the highest time derivative, we study a problem with integral conditions in
the time variable in the class of functions almost periodic in the space variables. A criterion of uniqueness and sufficient
conditions for the existence of the solution of this problem in different functional spaces are established. We use the metric
approach to solve the problem of small denominators encountered in the construction of the solution.
Citation Example:Kuz A. M., Ptashnik B. I. Problem with integral conditions in the time variable for Sobolevtype
system of equations with constant coefficients // Ukr. Mat. Zh. - 2017. - 69, № 4. - pp. 530-549.