Existence and global attractivity of positive periodic solution of an impulsive delay differential equation

2004 ◽  
Vol 83 (12) ◽  
pp. 1279-1290 ◽  
Author(s):  
Hai-Feng Huo ◽  
Wang-Tong Li ◽  
Xinzhi Liu †
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Delay Differential Equation ◽  
Global Attractivity ◽  
Positive Periodic Solution ◽  
Impulsive Delay ◽  
Impulsive Delay Differential Equation ◽  
Delay Differential

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.

scholarly journals Oscillation of impulsive delay differential equations and applications to population dynamics

2005 ◽  
Vol 46 (4) ◽  
pp. 545-554 ◽  
Author(s):  
Jurang Yan ◽  
Aimin Zhao ◽  
Linping Peng
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Impulsive Delay Differential Equations ◽  
Impulsive Delay ◽  
Impulsive Delay Differential Equation ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Nonlinear Delay Differential Equation ◽  
Nonlinear Delay ◽  
Oscillation And Nonoscillation

AbstractThe main result of this paper is that the oscillation and nonoscillation properties of a nonlinear impulsive delay differential equation are equivalent respectively to the oscillation and nonoscillation of a corresponding nonlinear delay differential equation without impulse effects. An explicit necessary and sufficient condition for the oscillation of a nonlinear impulsive delay differential equation is obtained.

scholarly journals Global attractivity of positive periodic solutions for an impulsive delay periodic “food limited” population model

2006 ◽  
Vol 2006 ◽  
pp. 1-10 ◽  
Author(s):  
Jian Song
Keyword(s):  
Global Attractivity ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Delay Equation ◽  
Periodic Functions ◽  
Globally Asymptotically Stable ◽  
Periodic Property ◽  
Impulsive Delay ◽  
Impulsive Delay Differential Equation ◽  
Delay Differential

We will consider the following nonlinear impulsive delay differential equationN′(t)=r(t)N(t)((K(t)−N(t−mw))/(K(t)+λ(t)N(t−mw))), a.e.t>0,t≠tk,N(tk+)=(1+bk)N(tk),K=1,2,…, wheremis a positive integer,r(t),K(t),λ(t)are positive periodic functions of periodicω. In the nondelay case(m=0), we show that the above equation has a unique positive periodic solutionN*(t)which is globally asymptotically stable. In the delay case, we present sufficient conditions for the global attractivity ofN*(t). Our results imply that under the appropriate periodic impulsive perturbations, the impulsive delay equation preserves the original periodic property of the nonimpulsive delay equation. In particular, our work extends and improves some known results.

scholarly journals Oscillation and Periodicity of a Second Order Impulsive Delay Differential Equation with a Piecewise Constant Argument

2017 ◽  
Vol 25 (2) ◽  
pp. 89-98
Author(s):  
Gizem S. Oztepe ◽  
Fatma Karakoc ◽  
Huseyin Bereketoglu
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Second Order ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Impulsive Delay ◽  
Impulsive Delay Differential Equation ◽  
Delay Differential ◽  
Constant Argument

Abstract This paper concerns with the existence of the solutions of a second order impulsive delay differential equation with a piecewise constant argument. Moreover, oscillation, nonoscillation and periodicity of the solutions are investigated.

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