A Problem with Condition Containing an Integral Term for a Parabolic-Hyperbolic Equation

In a layer obtained as the Cartesian product of an interval [-T-1 ,T-2], T-1 ,T-2 > 0, and a space R (p) , p >= 1, we study a problem with nonlocal condition in the time variable containing an integral term for a mixed parabolic-hyperbolic equation in the class of functions almost periodic in the space variables. For this problem, we establish a criterion of uniqueness and sufficient conditions for the existence of solutions. To solve the problem of small denominators encountered in the construction of the solution, we use the metric approach.