Approximate Method of Construction of Almost Periodic Solutions of Linear Systems of Differential Equations, Defined on the Infinite-Dimensional Torus

• Date: 2020
• Main Author: Теплінський, Юрій
• Format: Article
• Language: Ukrainian
• Published: Кам'янець-Подільський національний університет імені Івана Огієнка 2020
• Online Access: http://mcm-math.kpnu.edu.ua/article/view/224959
• Journal Title: Mathematical and computer modelling. Series: Physical and mathematical sciences

It is known that a large number of application problems in different sections of mathematics, physics, technology needs research of the problems of vibratorial solutions of differential systems, which are their mathematical models. In our time, the oscillled motions of dynamical systems by V. V. Nemytsky are called their recurrent movements, including quasi-periodic and almost-periodic movements. The fundamental theorem of Amerio and Favar is widely known, which refers to the existence of nearly-periodic solutions of nonlinear and linear systems. Later it became clear that the issue of such solutions is closely related to the existence of such systems of other facilities, for which construction is convenient to use the method of Green-Samoilenko function. Here the linear system of differential equations is considered, which is defined on the infinite-dimensional Tory (the case of the angular frequency base for the corner variable), and the relative normal variable, this system can be both finite and angular. The problem lies in in finding the sufficient conditions, in which the specified system of equations has almost-periodic family in the sense of Bohr solutions, each of which can be adapted to the predefined accuracy of quasi-periodic in the sense of Bol solution of corresponding shortened by the angular variable of the system of equations, which is defined on a finite-dimensional Tory.