Problem with integral conditions with respect to time for Shilov parabolic systems of equations (Q2808434)

In the domain being a Cartesian product of the segment \([0,T]\) and the space \(\mathbb R^p\), a problem containing integral conditions with respect to time coordinate is considered for Shilov parabolic systems of equations in the class of functions almost periodic with respect to space variables. For the problem solution a uniqueness criterion is found and sufficient existence conditions are established. To solve the small denominators problem, arising while constructing the problem solution, a metric approach is applied.