On the Boundedness of Solutions of a Quasilinear System of Ordinary Differential Equations
Author(s):
Ergashboy Mukhamadiev
Doctor of Physical and Mathematical Sciences,Professor,
Professor of the Department of Mathematics,
Vologda State University.
Russia, 160000, Vologda, st. Lenina, 15.
emuhamadiev@rambler.ru
Alizhon Nabidjanovich Naimov
Doctor of Physical and Mathematical Sciences,Professor,
Professor of the Department of Mathematics,
Vologda State University.
Russia, 160000, Vologda, st. Lenina, 15.
naimovan@vogu35.ru
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.
Keywords
- bounded solution
- limit equation method
- observed values
- quasi-linear system of equations
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