Problem with Integral Conditions in the Time Variable for a Sobolev-Type System of Equations with Constant Coefficients

Abstract

In a domain obtained as a Cartesian product of an interval [0,T] and the space ℝ p , p ∈ ℕ, for a system of equations (with constant coefficients) unsolved with respect to the highest time derivative, we study the problem with integral conditions in the time variable for a class of functions almost periodic in the space variables. A criterion of uniqueness and sufficient conditions for the existence of 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.