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.

scholarly journals Delay differential equations of odd order satisfying property Pk

1975 ◽  
Vol 20 (4) ◽  
pp. 451-467
Author(s):  
Raymond D. Terry
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Odd Order ◽  
Delay Differential ◽  
Satisfying Property

AbstractThe property Pk(K = 0,1,…,n) is formulated. For k = 0, n this property reduces to conditions A and B defined by Kiguradze (1962) for a class of ordinary differential equations. Sufficient conditions are then given which guarentee that a class of delay differential equations of odd order possesses property Pk. The property PK is also seen to be useful in reducing the number of types of positve solutions of a related nonhomogeneous delay differential equation.

scholarly journals Global attractivity of a class of delay differential equations with impulses

2003 ◽  
Vol 45 (2) ◽  
pp. 271-284 ◽  
Author(s):  
Yuji Liu ◽  
Binggen Zhang
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Impulsive Delay ◽  
Impulsive Delay Differential Equation ◽  
Delay Differential

AbstractIn this paper, we study the global attractivity of the zero solution of a particular impulsive delay differential equation. Some sufficient conditions that guarantee every solution of the equation converges to zero are obtained.

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 Periodic solutions for periodic second-order differential equations with variable potentials

2018 ◽  
Vol 24 (2) ◽  
pp. 127-137
Author(s):  
Jaume Llibre ◽  
Ammar Makhlouf
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Second Order Differential Equation ◽  
Existence Of Periodic Solutions

Abstract We provide sufficient conditions for the existence of periodic solutions of the second-order differential equation with variable potentials {-(px^{\prime})^{\prime}(t)-r(t)p(t)x^{\prime}(t)+q(t)x(t)=f(t,x(t))} , where the functions {p(t)>0} , {q(t)} , {r(t)} and {f(t,x)} are {\mathcal{C}^{2}} and T-periodic in the variable t.

Oscillations of Neutral Delay Differential Equations

1986 ◽  
Vol 29 (4) ◽  
pp. 438-445 ◽  
Author(s):  
G. Ladas ◽  
Y. G. Sficas
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Oscillatory Behavior ◽  
Neutral Delay ◽  
Neutral Delay Differential Equation ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

AbstractThe oscillatory behavior of the solutions of the neutral delay differential equationwhere p, τ, and a are positive constants and Q ∊ C([t0, ∞), ℝ+), are studied.

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

1986 ◽  
Vol 102 (3-4) ◽  
pp. 259-262 ◽  
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.

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 Periodic Solutions of a System of Delay Differential Equations for a Small Delay

2002 ◽  
Vol 7 (2) ◽  
pp. 295
Author(s):  
Adu A.M. Wasike ◽  
Wandera Ogana
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Delay Differential Equations ◽  
Original System ◽  
System Of Equations ◽  
Asymptotically Stable ◽  
Stable Periodic Solution ◽  
Stable Periodic ◽  
Delay Differential

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.   

scholarly journals Solution Of Singularly Perturbed Delay Differential Equations Using Liouville Green Transformation

2021 ◽  
Vol 12 (4) ◽  
pp. 325-335
Author(s):  
M. Adilaxmi , Et. al.
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Perturbation Problem ◽  
Delay Differential ◽  
Singularly Perturbation ◽  
The Given

This paper envisages the use of Liouville Green Transformation to find the solution of singularly perturbed delay differential equations. First, using Taylor series, the given singularly perturbed delay differential equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. The method is demonstrated by implementing several model examples by taking various values for the delay parameter and perturbation parameter.

scholarly journals Existence of periodic solution for first order nonlinear neutral delay equations

2001 ◽  
Vol 14 (2) ◽  
pp. 189-194 ◽  
Author(s):  
Genqiang Wang ◽  
Jurang Yan
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Neutral Delay ◽  
First Order ◽  
Neutral Delay Differential Equation ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper by using the coincidence degree theory, sufficient conditions are given for the existence of periodic solutions of the first order nonlinear neutral delay differential equation.

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