# Kuz A. M.

### Problem with integral conditions in the time variable for Sobolevtype system of equations with constant coefficients

Ukr. Mat. Zh. - 2017. - 69, № 4. - pp. 530-549

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

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

Ukr. Mat. Zh. - 2015. - 67, № 5. - pp. 635-644

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.

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

Ukr. Mat. Zh. - 2013. - 65, № 2. - pp. 252-265

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.