Stable Periodic Solutions for Two-Dimensional Linear Delay Differential Equations

We prove the existence of an asymptotically stable periodic solution of a system of delay differential equations with a small time delay t > 0. To achieve this, we transform the system of equations into a system of perturbed ordinary differential equations and then use perturbation results to show the existence of an asymptotically stable periodic solution. This approach is contingent on the fact that the system of equations with t = 0 has a stable limit cycle. We also provide a comparative study of the solutions of the original system and the perturbed system. This comparison lays the ground for proving the existence of periodic solutions of the original system by Schauder's fixed point theorem.

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Maximum Principles for Periodic Solutions of Linear Delay Differential Equations

Differential-Difference Equations/Differential-Differenzengleichungen - International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique ◽

10.1007/978-3-0348-6767-2_2 ◽

1983 ◽

pp. 19-24 ◽

Cited By ~ 4

Author(s):

A. Bellen ◽

M. Zennaro

Keyword(s):

Differential Equations ◽

Periodic Solutions ◽

Delay Differential Equations ◽

Maximum Principles ◽

Linear Delay ◽

Delay Differential

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Growth on Meromorphic Solutions of Non-linear Delay Differential Equations

Bulletin of the Belgian Mathematical Society - Simon Stevin ◽

10.36045/bbms/1553047233 ◽

2019 ◽

Vol 26 (1) ◽

pp. 131-147 ◽

Cited By ~ 2

Author(s):

Pei-Chu Hu ◽

Qiong-Yan Wang

Keyword(s):

Differential Equations ◽

Delay Differential Equations ◽

Meromorphic Solutions ◽

Linear Delay ◽

Non Linear ◽

Delay Differential

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A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽

10.2298/fil1711157a ◽

2017 ◽

Vol 31 (11) ◽

pp. 3157-3172

Author(s):

Mujahid Abbas ◽

Bahru Leyew ◽

Safeer Khan

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Fixed Points ◽

Periodic Solutions ◽

Metric Space ◽

Delay Differential Equations ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Existence Of Periodic Solutions ◽

Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

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