On the Boundedness of Solutions of a Quasilinear System of Ordinary Differential Equations

Abstract

In the paper, the question of the boundedness of an arbitrary solution of a quasilinear system of ordinary differential equations is investigated under boundedness of the observed values of the solution. The observed values of the solution are a finite set of scalar products of the solution with given vectors. In terms of the properties of the matrix of coefficients of the system of equations and the matrix of coefficients of observed values, theorems on the boundedness of an arbitrary solution with boundedness of the observed values are formulated and proved. The novelty of this paper is that using the method of limit equations, estimates are derived from which the boundedness or stability follows an arbitrary solution of a quasilinear system in terms of boundedness or stability of the observed values of the solution.