Integral manifolds of systems of differential equations with a random right-hand side in a Banach space

1992 ◽  
Vol 44 (1) ◽  
pp. 12-16 ◽  
Author(s):  
V. G. Kolomiets ◽  
A. I. Mel'nikov
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Systems Of Differential Equations ◽  
Right Hand ◽  
Integral Manifolds

Existence of integral manifolds for impulsive differential equations in a Banach space

1989 ◽  
Vol 28 (7) ◽  
pp. 815-833 ◽  
Author(s):  
D. D. Bainov ◽  
S. I. Kostadinov ◽  
Nguy�� H�ng Th�i ◽  
P. P. Zabreiko
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Impulsive Differential Equations ◽  
Integral Manifolds

CONTINUOUS DEPENDENCE ON A PARAMETER OF THE SOLUTIONS OF IMPULSIVE DIFFERENTIAL EQUATIONS IN A BANACH SPACE

1993 ◽  
Vol 03 (04) ◽  
pp. 477-483
Author(s):  
D.D. BAINOV ◽  
S.I. KOSTADINOV ◽  
NGUYEN VAN MINH ◽  
P.P. ZABREIKO
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Differential Equations ◽  
Small Parameter ◽  
Continuous Dependence ◽  
Impulsive Differential Equation ◽  
Impulsive Differential Equations ◽  
Right Hand ◽  
Dependence On A Parameter ◽  
The Right

Continuous dependence of the solutions of an impulsive differential equation on a small parameter is proved under the assumption that the right-hand side of the equation and the impulse operators satisfy conditions of Lipschitz type.

scholarly journals CONSTRUCTION OF STABILITY AREAS FOR CONTROLLED SYSTEMS WITH PARAMETRIC AND DYNAMIC UNCERTAINTY

2021 ◽  
pp. 117-122
Author(s):  
Alla Savranska ◽  
Oleksandr Denisenko
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Small Parameter ◽  
Singularly Perturbed ◽  
Singularly Perturbed Systems ◽  
Systems Of Differential Equations ◽  
Right Hand ◽  
Perturbed Systems ◽  
Small Factor ◽  
The Right

The subject of research in the article is sigularly perturbed controllable systems of differential equations containing terms with a small parameters on the right-hand side, which are not completely known, but only satisfy some constraints. The aim of the work is to expand the study of the behavior of solutions of singularly perturbed systems of differential equations to the case when the system is influenced not only by dynamic (small factor at the derivative) but also parametric (small factor at the right side of equations) uncertainties and to determine conditions under which such systems will be asymptotically resistant to any perturbations, estimate the upper limit of the small parameter, so that for all values of this parameter less than the obtained estimate, the undisturbed solution of the system was asymptotically stable. The following problems are solved in the article: singularly perturbed systems of differential equations with regular perturbations in the form of terms with a small parameter in the right-hand sides, which are not fully known, are investigated; an estimate is made of the areas of asymptotic stability of the unperturbed solution of such systems, that is, the class of systems that can be investigated for stability is expanded, the formulas obtained that allow one to analyze the asymptotic stability of solutions to systems even under conditions of incomplete information about the perturbations acting on them. The following methods are used: mathematical modeling of complex control systems; vector Lyapunov functions investigation of asymptotic stability of solutions of systems of differential equations. The following results were obtained: an estimate was made for the upper bound of a small parameter for sigularly perturbed systems of differential equations with fully known parametric (fully known) and dynamic uncertainties, such that for all values of this parameter less than the obtained estimate, such an unperturbed solution is asymptotically stable; a theorem is proved in which sufficient conditions for the uniform asymptotic stability of such a system are formulated. Conclusions: the method of vector Lyapunov functions extends to the class of singularly perturbed systems of differential equations with a small factor in the right-hand sides, which are not completely known, but only satisfy certain constraints.

Periodic solutions of systems of differential equations with random right-hand sides

1997 ◽  
Vol 49 (2) ◽  
pp. 247-252
Author(s):  
D. I. Martynyuk ◽  
V. Ya. Danilov ◽  
A. N. Stanzhitskii
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Systems Of Differential Equations ◽  
Right Hand
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