A problem with integral conditions with respect to time for Garding hyperbolic equations

Abstract

In a domain that is the Cartesian product of an interval $[0,T]$ and the space $\mathbb{R}^p$, we investigate a problem for Garding hyperbolic equations having constant coefficients with integral conditions with respect to the time variable in a class of functions almost periodic in the space variables. A criterion for the uniqueness and sufficient conditions for the existence of a solution of the problem in different functional spaces are established. To solve the problem of small denominators that arises in the solution of the problem, the metric approach is used.