Existence and Uniqueness of Periodic Solutions for (2k)th-Order Delay Differential Equations

2012 ◽  
Vol 538-541 ◽  
pp. 2500-2503
Author(s):  
Xin Liang ◽  
Fu Zhong Cong ◽  
Ming Juan Ma ◽  
Yu Zhang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fourier Analysis ◽  
Periodic Solutions ◽  
Delay Differential Equations ◽  
Existence And Uniqueness ◽  
Even Order ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

The existence of periodic solutions for a class of even order delay differential equations is obtained. It is useful in the delay problem of wireless beaconage. The proofs are based on combining a method of Fourier analysis with Schauder fixed point theorem. This generalizes results developed by W. Layton to high order equations

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

Filomat ◽  
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.

scholarly journals Existence and Uniqueness of Periodic Solutions for Second Order Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Yuanhong Wei
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Function Space ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Second Order ◽  
Second Order Differential Equations

We study some second order ordinary differential equations. We establish the existence and uniqueness in some appropriate function space. By using Schauder’s fixed-point theorem, new results on the existence and uniqueness of periodic solutions are obtained.

Existence of periodic solutions for a system of delay differential equations

2009 ◽  
Vol 71 (12) ◽  
pp. 6222-6231 ◽  
Author(s):  
Cheng-Hsiung Hsu ◽  
Suh-Yuh Yang ◽  
Ting-Hui Yang ◽  
Tzi-Sheng Yang
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Delay Differential Equations ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

scholarly journals Multiplicity of Periodic Solutions for Third-Order Nonlinear Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Xuxin Yang ◽  
Weibing Wang ◽  
Dingyang Lv
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Operator ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Integrodifferential Equation ◽  
Nonlinear Differential Equations ◽  
Third Order ◽  
Existence Of Periodic Solutions ◽  
Linear Integral

We study the existence of periodic solutions for third-order nonlinear differential equations. The method of proof relies on Schauder’s fixed point theorem applied in a novel way, where the original equation is transformed into second-order integrodifferential equation through a linear integral operator. Finally, examples are presented to illustrate applications of the main results.

scholarly journals On Periodic Solutions of Delay Differential Equations with Impulses

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 523 ◽  
Author(s):  
Mostafa Bachar
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Distributed Delay ◽  
Impulsive Delay Differential Equations ◽  
Impulsive Delay ◽  
Delay Differential ◽  
Distributed Delay Differential Equations

The purpose of this paper is to study the nonlinear distributed delay differential equations with impulses effects in the vectorial regulated Banach spaces R ( [ − r , 0 ] , R n ) . The existence of the periodic solution of impulsive delay differential equations is obtained by using the Schäffer fixed point theorem in regulated space R ( [ − r , 0 ] , R n ) .

scholarly journals An existence theorem for nonlinear delay differential equations

1989 ◽  
Vol 2 (2) ◽  
pp. 85-89
Author(s):  
Krishnan Balachandran
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Existence Theorem ◽  
Delay Differential Equations ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Nonlinear Delay Differential Equations ◽  
Delay Differential ◽  
Nonlinear Delay

In this paper we prove a theorem on the existence of solutions of nonlinear delay differential equations, with implicit derivatives. The result is established using the measure of noncompactness of a set and Darbo's fixed point theorem.

PERIODIC SOLUTION FOR GENERALIZED HIGH-ORDER DELAY DIFFERENTIAL EQUATIONS

2010 ◽  
Vol 03 (01) ◽  
pp. 31-43
Author(s):  
Zhibo Cheng ◽  
Jingli Ren ◽  
Stefan Siegmund
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Existence Of Periodic Solutions ◽  
Delay Differential ◽  
New Inequalities

In this paper we consider a generalized n-th order delay differential equation, by applying Mawhin's continuation theory and some new inequalities, we obtain sufficient conditions for the existence of periodic solutions. Moreover, an example is given to illustrate the results.

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