scholarly journals A Variation-of-Constants Formula for Abstract Functional Differential Equations in the Phase Space

2002 ◽  
Vol 179 (1) ◽  
pp. 336-355 ◽  
Author(s):  
Yoshiyuki Hino ◽  
Satoru Murakami ◽  
Toshiki Naito ◽  
Nguyen Van Minh
Keyword(s):  
Phase Space ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Variation Of Constants Formula ◽  
Variation Of Constants ◽  
Functional Differential

Variation of constants for hybrid systems of functional differential equations

1995 ◽  
Vol 125 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Jack K. Hale ◽  
Wenzhang Huang
Keyword(s):  
Differential Equations ◽  
Hybrid Systems ◽  
Difference Equations ◽  
Delay Differential Equations ◽  
Functional Equations ◽  
Functional Differential Equations ◽  
Variation Of Constants Formula ◽  
Variation Of Constants ◽  
Functional Differential ◽  
Delay Differential

The objective is to derive a variation of constants formula for systems of functional differential equations (or delay differential equations) coupled with functional equations (or difference equations). The difficulties arise because of the constraints imposed by the functional equations.

Compact boundedness in periodic functional differential equations with infinite delay

1990 ◽  
Vol 114 (3-4) ◽  
pp. 291-297
Author(s):  
Junji Kato
Keyword(s):  
Phase Space ◽  
Differential Equations ◽  
Infinite Delay ◽  
Functional Differential Equations ◽  
Periodic Systems ◽  
Compact Set ◽  
Ultimate Boundedness ◽  
Local Compactness ◽  
Non Local ◽  
Functional Differential

SynopsisIt is the aim of this article to consider some problems arising from the non local-compactness of the phase space for functional differential equations. The compact boundedness, that is, the boundedness depending on each compact set involving the initial values, is proved to be implied from the ultimate boundedness for periodic systems of functional differential equations on Cγ: = {φ ∊ C((–∞,0]) Note that it is known that the compactness cannot be dropped in the above. An example is also given to show that the asymptotic stability is not necessarily uniform even for periodic functional differential equations on Co.

scholarly journals LINEAR AUTONOMOUS NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS IN THE PHASE SPACE OF REGULATED FUNCTIONS

1994 ◽  
Vol 25 (3) ◽  
pp. 195-207
Author(s):  
LUIZ FICHMANN
Keyword(s):  
Phase Space ◽  
Differential Equations ◽  
Linear Equation ◽  
Functional Differential Equations ◽  
Continuous Functions ◽  
Neutral Functional Differential Equations ◽  
Functional Differential ◽  
Regulated Functions ◽  
Natural Description

We extend the natural description of the spectrum for the flow of the linear equation $\frac{d}{dt}Dx_t=Lx_t$ from the context of continuous functions to the context of regulated right-continuous functions.

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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