The Problem of Bounded Solutions for N-Th Order Vector-Matrix Differential Equations

This article investigates the problems of existence and uniqueness of bounded solutions for a system of n-th order nonlinear vector-matrix differential equations. In the course of the study, sufficient conditions ensuring the existence, uniqueness, and boundedness of solutions of the considered system are established and formulated in the form of main theorems. The obtained results are justified on the basis of Banach’s fixed point principle and the method of integral equations. Furthermore, the significance of the derived estimates in the investigation of qualitative properties of solutions to differential systems is demonstrated.