ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

On the Theory of the Existence of Bounded Solutions of Systems of Nonlinear 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:

We formulate and prove necessary and sufficient conditions that provide an a priori estimate for bounded solutions for one class of systems of nonlinear ordinary differential equations with the main positively homogeneous part. criterion for the existence of bounded solutions is proved using the method of guiding functions and Vazhevski's method under the condition of an a priori estimate. These results refine and generalize the previously obtained results of the authors in the multidimensional case.

Keywords

References:

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