A Problem with Integral Conditions with Respect to Time for Shilov Parabolic Systems of Equations

详细

In a domain specified in the form of the Cartesian product of an interval [0,T] and a space ℝ^p, we study a problem with integral conditions with respect to the time coordinate for Shilov parabolic systems of equations in the class of functions almost periodic with respect to the space variables. We establish a criterion of uniqueness and sufficient conditions for the existence of a solution of the problem. To solve the problem of small denominators encountered in the construction of the solution, we apply the metric approach.