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.

Periodic solutions to functional differential equations

1985 ◽  
Vol 101 (3-4) ◽  
pp. 253-271 ◽  
Author(s):  
O. A. Arino ◽  
T. A. Burton ◽  
J. R. Haddock
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Uniform Boundedness ◽  
Continuous Functions ◽  
Ultimate Boundedness ◽  
Space Of Continuous Functions ◽  
Uniform Ultimate Boundedness ◽  
Functional Differential ◽  
Image Position

SynopsisWe consider a system of functional differential equationswhere G: R × B → Rn is T periodic in t and B is a certain phase space of continuous functions that map (−∞, 0[ into Rn. The concepts of B-uniform boundedness and B-uniform ultimate boundedness are introduced, and sufficient conditions are given for the existence of a T-periodic solution to (1.1). Several examples are given to illustrate the main theorem.

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