Lyapunov’s direct method for linear systems of functional-differential equations in Sobolev space

2014 ◽  
Vol 55 (4) ◽  
pp. 696-705
Author(s):  
R. K. Romanovsky ◽  
E. M. Nazaruk
Keyword(s):  
Sobolev Space ◽  
Differential Equations ◽  
Linear Systems ◽  
Direct Method ◽  
Functional Differential Equations ◽  
Lyapunov’S Direct Method ◽  
Functional Differential

Asymptotic stability criteria for delay-differential equations

1988 ◽  
Vol 110 (1-2) ◽  
pp. 31-44
Author(s):  
L.C. Becker ◽  
T.A. Burton
Keyword(s):  
Differential Equations ◽  
Direct Method ◽  
Infinite Delay ◽  
Functional Differential Equations ◽  
State Variables ◽  
Stability Criteria ◽  
Bounded State ◽  
Functional Differential ◽  
Delay Differential ◽  
Liapunov's Direct Method

SynopsisThis paper is concerned with the problem of showing uniform stability and equiasymptotic stability of thezero solution of functional differential equations with either finite or infinite delay. The investigations are based on Liapunov's direct method and attention is focused on those equations whose right-hand sides are unbounded for bounded state variables.

scholarly journals Stability of the solutions of impulsive functional-differential equations by Lyapunov's direct method

2001 ◽  
Vol 43 (2) ◽  
pp. 269-278 ◽  
Author(s):  
D. D. Bainov ◽  
I. M. Stamova
Keyword(s):  
Differential Equations ◽  
Lyapunov Functions ◽  
Direct Method ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Continuous Functions ◽  
Piecewise Continuous ◽  
Functional Differential ◽  
The Stability

AbstractWe consider the stability of the zero solution of a system of impulsive functional-differential equations. By means of piecewise continuous functions, which are generalizations of classical Lyapunov functions, and using a technique due to Razumikhin, sufficient conditions are found for stability, uniform stability and asymptotical stability of the zero solution of these equations. Applications to impulsive population dynamics are also discussed.

Stability of Implicit Difference Equations Generated by Parabolic Functional Differential Problems

2007 ◽  
Vol 7 (1) ◽  
pp. 68-82
Author(s):  
K. Kropielnicka
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Initial Boundary ◽  
Numerical Examples ◽  
Convergence Results ◽  
Nonlinear Parabolic ◽  
Implicit Difference Methods ◽  
Neumann Type ◽  
Difference Methods ◽  
Functional Differential

AbstractA general class of implicit difference methods for nonlinear parabolic functional differential equations with initial boundary conditions of the Neumann type is constructed. Convergence results are proved by means of consistency and stability arguments. It is assumed that given functions satisfy nonlinear estimates of Perron type with respect to functional variables. Differential equations with deviated variables and differential integral problems can be obtained from a general model by specializing given operators. The results are illustrated by numerical examples.

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