On periodic solutions to autonomous retarded functional differential equations

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.

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On the existence of periodic solutions for autonomous retarded functional differential equations on R2

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500026342 ◽

1986 ◽

Vol 102 (3-4) ◽

pp. 259-262 ◽

Cited By ~ 1

Author(s):

J. G. Dos Reis ◽

R. L. S. Baroni

Keyword(s):

Differential Equation ◽

Periodic Solution ◽

Differential Equations ◽

Periodic Solutions ◽

Functional Differential Equations ◽

Continuous Functions ◽

Retarded Functional Differential Equations ◽

Existence Of Periodic Solutions ◽

Functional Differential

SynopsisLet Ca be the set of all the continuous functions from the interval [−r, 0] on the sphere of radius a, on the plane. We prove, under certains conditions, that a retarded autonomous differential equation that leaves Ca invariant has a non-constant periodic solution.

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On Periodic Solutions of Nonlinear Functional Differential Equations

Georgian Mathematical Journal ◽

10.1515/gmj.1999.45 ◽

1999 ◽

Vol 6 (1) ◽

pp. 45-64

Author(s):

I. Kiguradze ◽

B. Půža

Keyword(s):

Differential Equation ◽

Periodic Solution ◽

Periodic Solutions ◽

Existence And Uniqueness ◽

Functional Differential Equations ◽

Sufficient Conditions ◽

Continuous Operator ◽

Nonlinear Functional ◽

Continuous Vector ◽

Functional Differential

Abstract Sufficient conditions are established for the existence and uniqueness of an ω-periodic solution of the functional differential equation where f is a continuous operator acting from the space of n-dimensional ω-periodic continuous vector functions into the space of n-dimensional ω-periodic and summable on [0, ω] vector functions.

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The necessary and sufficient conditions for the existence of periodic solutions of a type of neutral functional differential equations

Acta Mathematicae Applicatae Sinica English Series ◽

10.1007/bf02080205 ◽

1991 ◽

Vol 7 (1) ◽

pp. 74-79

Author(s):

Yi Zhang ◽

Yi Zhang

Keyword(s):

Differential Equations ◽

Periodic Solutions ◽

Functional Differential Equations ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Neutral Functional Differential Equations ◽

Existence Of Periodic Solutions ◽

Functional Differential ◽

Necessary And Sufficient

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On the Almost Periodic Solutions of Differential Equations on Hilbert Spaces

International Journal of Differential Equations ◽

10.1155/2009/575939 ◽

2009 ◽

Vol 2009 ◽

pp. 1-11 ◽

Cited By ~ 1

Author(s):

Nguyen Thanh Lan

Keyword(s):

Differential Equation ◽

Hilbert Space ◽

Periodic Solution ◽

Periodic Solutions ◽

Hilbert Spaces ◽

Sufficient Conditions ◽

Almost Periodic Solution ◽

Almost Periodic Solutions ◽

Almost Periodic ◽

Necessary And Sufficient

For the differential equation , on a Hilbert space , we find the necessary and sufficient conditions that the above-mentioned equation has a unique almost periodic solution. Some applications are also given.

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

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500011501 ◽

1979 ◽

Vol 83 (3-4) ◽

pp. 189-198 ◽

Cited By ~ 4

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

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A necessary and sufficient condition for well-posedness of initial value problems of retarded functional differential equations

Journal of Differential Equations ◽

10.1016/j.jde.2017.04.038 ◽

2017 ◽

Vol 263 (6) ◽

pp. 3491-3532 ◽

Cited By ~ 3

Author(s):

Junya Nishiguchi

Keyword(s):

Differential Equations ◽

Initial Value Problems ◽

Functional Differential Equations ◽

Well Posedness ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Initial Value ◽

Retarded Functional Differential Equations ◽

Functional Differential ◽

Necessary And Sufficient

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

Discrete Dynamics in Nature and Society ◽

10.1155/2020/6569308 ◽

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.

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Anti-periodic solutions of nonlinear first order impulsive functional differential equations

Mathematica Slovaca ◽

10.2478/s12175-012-0039-4 ◽

2012 ◽

Vol 62 (4) ◽

Cited By ~ 1

Author(s):

Yuji Liu

Keyword(s):

Periodic Solution ◽

Differential Equations ◽

Periodic Solutions ◽

Functional Differential Equations ◽

Sufficient Conditions ◽

Existence Results ◽

First Order ◽

Functional Differential

AbstractThe existence of anti-periodic solutions of the following nonlinear impulsive functional differential equations $$ x'(t) + a(t)x(t) = f(t,x(t),x(\alpha _1 (t)), \ldots ,x(\alpha _n (t))),t \in \mathbb{R},\Delta x(t_k ) = I_k (x(t_k )),k \in \mathbb{Z} $$ is studied. Sufficient conditions for the existence of at least one anti-periodic solution of the mentioned equation are established. Several new existence results are obtained.

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