On Lipschitz stability for comparison systems of differential equations via limiting equation

2005 ◽  
Vol 163 (3) ◽  
pp. 1061-1067 ◽  
Author(s):  
A.A. Soliman
Keyword(s):  
Differential Equations ◽  
Lipschitz Stability ◽  
Systems Of Differential Equations

scholarly journals Cone valued Lyapunov functions and Lipschitz stability of nonlinear systems of differential equations

1996 ◽  
Vol 19 (3) ◽  
pp. 435-440
Author(s):  
Olusola Akinyele
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Differential Equations ◽  
Lyapunov Functions ◽  
Practical Stability ◽  
Lipschitz Stability ◽  
Comparison Result ◽  
Systems Of Differential Equations ◽  
New Concepts ◽  
Perturbed Systems

We introduce a new comparison result which will be an important tool when we apply cone valued Lyapunov like functions. We also introduce new concepts ofϕ0-uniform Lipschitz stability and(λ,λ,ϕ0)-practical stability and employ our comparison result to carry out stability analysis of nonlinear systems. Our results are also applicable to nonlinear perturbed systems.

scholarly journals On eventual stability of impulsive systems of differential equations

2001 ◽  
Vol 27 (8) ◽  
pp. 485-494
Author(s):  
A. A. Soliman
Keyword(s):  
Differential Equations ◽  
Lipschitz Stability ◽  
Impulsive Systems ◽  
Systems Of Differential Equations ◽  
Eventual Stability

The notions of Lipschitz stability of impulsive systems of differential equations are extended and the notions of eventual stability are introduced. New notions called eventual and eventual Lipschitz stability. We give some criteria and results.

SOLUTION OF SOME SYSTEMS OF DIFFERENTIAL EQUATIONS IN MATHEMATICAL SYSTEM MAPLE

2013 ◽  
Vol 1 (05) ◽  
pp. 58-65
Author(s):  
Yunona Rinatovna Krakhmaleva ◽  
◽  
Gulzhan Kadyrkhanovna Dzhanabayeva ◽  
Keyword(s):  
Differential Equations ◽  
Systems Of Differential Equations ◽  
Mathematical System

On decomposability of countable systems of differential equations

1993 ◽  
Vol 45 (10) ◽  
pp. 1598-1608
Author(s):  
A. M. Samoilenko ◽  
Yu. V. Teplinskii
Keyword(s):  
Differential Equations ◽  
Systems Of Differential Equations

scholarly journals Differential Games for an Infinite 2-Systems of Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1467
Author(s):  
Muminjon Tukhtasinov ◽  
Gafurjan Ibragimov ◽  
Sarvinoz Kuchkarova ◽  
Risman Mat Hasim
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Differential Games ◽  
Differential Game ◽  
Infinite System ◽  
The State ◽  
Geometric Constraints ◽  
Control Parameters ◽  
Systems Of Differential Equations ◽  
Pursuit And Evasion

A pursuit differential game described by an infinite system of 2-systems is studied in Hilbert space l2. Geometric constraints are imposed on control parameters of pursuer and evader. The purpose of pursuer is to bring the state of the system to the origin of the Hilbert space l2 and the evader tries to prevent this. Differential game is completed if the state of the system reaches the origin of l2. The problem is to find a guaranteed pursuit and evasion times. We give an equation for the guaranteed pursuit time and propose an explicit strategy for the pursuer. Additionally, a guaranteed evasion time is found.

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