A star-shaped condition for stability of linear retarded functional differential equations†

1979 ◽  
Vol 83 (3-4) ◽  
pp. 189-198 ◽  
Author(s):  
Richard Silkowski
Keyword(s):  
Asymptotic Stability ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Retarded Functional Differential Equations ◽  
Region Of Stability ◽  
Linear Functional Differential Equation ◽  
Functional Differential ◽  
Image Position ◽  
Necessary And Sufficient

SYNOPSISSufficient conditions are developed for asymptotic stability of the autonomous linear functional differential equation of retarded type. If the asymptotic stability ofimplies the asymptotic stability ofthen these conditions are also necessary. Necessary and sufficient conditions are developed for the largest cone in the region of stability. These results are illustrated with the example

scholarly journals On periodic solutions to autonomous retarded functional differential equations

1990 ◽  
Vol 41 (3) ◽  
pp. 347-354
Author(s):  
Zhanyuan Hou
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Retarded Functional Differential Equations ◽  
Retarded Functional Differential Equation ◽  
Functional Differential ◽  
Necessary And Sufficient

Under the assumption that Ca = C([−r, 0], Sn−1(a)) is positively invariant for a > 0, two necessary and sufficient conditions are obtained for an autonomous retarded functional differential equation to have a non-trivial periodic solution in Ca. Moreover, a feasible sufficient condition is given, which is better for n = 2 than that given by Dos Reis and Baroni.

scholarly journals 19.—Asymptotic Stability for Some Functional Differential Equations

1976 ◽  
Vol 74 ◽  
pp. 253-255 ◽  
Author(s):  
Hans-Otto Walther ◽  
W. N. Everitt
Keyword(s):  
Differential Equation ◽  
Asymptotic Stability ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Characteristic Equation ◽  
Population Biology ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Linear Functional Differential Equation ◽  
Functional Differential

SynopsisFor a non-linear functional differential equation from population biology, a result on asymptotic stability is obtained by investigating the zeros of the characteristic equation of the linearised functional differential equation.

scholarly journals Asymptotic Stability of Neutral Set-Valued Functional Differential Equation by Fixed Point Method

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Junyan Bao ◽  
Peiguang Wang
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Asymptotic Stability ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Fixed Point Method ◽  
Stability Theorem ◽  
Point Method ◽  
Functional Differential ◽  
Necessary And Sufficient

This paper studies a class of nonlinear neutral set-valued functional differential equations. The globally asymptotic stability theorem with necessary and sufficient conditions is obtained via the fixed point method. Meanwhile, we give an example to illustrate the obtained result.

The weighted Cauchy problem for linear functional differential equations with strong singularities

2011 ◽  
Vol 18 (3) ◽  
pp. 577-586
Author(s):  
Zaza Sokhadze
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Initial Point ◽  
Higher Order ◽  
Well Posedness ◽  
Deviating Arguments ◽  
Functional Differential

Abstract The sufficient conditions of well-posedness of the weighted Cauchy problem for higher order linear functional differential equations with deviating arguments, whose coefficients have nonintegrable singularities at the initial point, are found.

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.

On Bounded Solutions of Systems of Linear Functional Differential Equations

1999 ◽  
Vol 6 (5) ◽  
pp. 429-440
Author(s):  
R. Hakl
Keyword(s):  
Differential Equations ◽  
Real Axis ◽  
Existence And Uniqueness ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Bounded Solutions ◽  
Functional Differential

Abstract Sufficient conditions of the existence and uniqueness of bounded on real axis solutions of systems of linear functional differential equations are established.

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