TY - JOUR AU - L. A. Vlasenko AU - A. G. Rutkas AU - A. O. Chikrii PY - 2022/02/21 Y2 - 2024/03/29 TI - Functional differential games with nonatomic difference operator JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 74 IS - 2 SE - Research articles DO - 10.37863/umzh.v74i2.6895 UR - https://umj.imath.kiev.ua/index.php/umj/article/view/6895 AB - UDC 517.9We study a differential game of approach in a system whose dynamics is describedby a linear functional differential equation. The coefficients of the equation are closed linear operators on Hilbert spaces. The operator multiplying the state derivative at the current time is generally non-invertible. The main assumption is a restriction imposed on the characteristic operator pencil of the equation on a ray of real the positive semi-axis. Solutions of the equation are represented with the help of a formula of variation of constants where the delay effect is taken into account by summing shift type operators. To obtain conditions for the approach of the system dynamic vector to a cylindrical terminal set, we use constraints on support functionals of two sets defined by the behavior of pursuer and evader.The paper contains an example to illustrate the differential game in a pseudoparabolic system described by a partial functional differential equation. ER -