Uniform stability with respect to the impulsive perturbations of the solutions of impulsive differential equations

1992 ◽  
Vol 31 (2) ◽  
pp. 363-372
Author(s):  
A. B. Dishliev ◽  
D. D. Bainov
Keyword(s):  
Differential Equations ◽  
Impulsive Differential Equations ◽  
Uniform Stability ◽  
Impulsive Perturbations

scholarly journals Oscillation of Second-Order Sublinear Impulsive Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
A. Zafer
Keyword(s):  
Differential Equations ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Oscillation Criteria ◽  
Impulsive Perturbations

Oscillation criteria obtained by Kusano and Onose (1973) and by Belohorec (1969) are extended to second-order sublinear impulsive differential equations of Emden-Fowler type:x″(t)+p(t)|x(τ(t))|α-1x(τ(t))=0,t≠θk;Δx'(t)|t=θk+qk|x(τ(θk))|α-1x(τ(θk))=0;Δx(t)|t=θk=0,  (0<α<1)by considering the casesτ(t)≤tandτ(t)=t, respectively. Examples are inserted to show how impulsive perturbations greatly affect the oscillation behavior of the solutions.

scholarly journals ψ-UNIFORM STABILITY FOR LINEAR IMPULSIVE DIFFERENTIAL EQUATIONS

2014 ◽  
Vol 27 (3) ◽  
pp. 495-502
Author(s):  
Yinhua Cui ◽  
Sung Sook Kim ◽  
Yoon Hoe Goo
Keyword(s):  
Differential Equations ◽  
Impulsive Differential Equations ◽  
Uniform Stability

scholarly journals Dynamics of an Almost Periodic Food Chain System with Impulsive Effects

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Yaqin Li ◽  
Wenquan Wu ◽  
Tianwei Zhang
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Food Chain ◽  
Impulsive Differential Equations ◽  
Almost Periodic Solution ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Chain System ◽  
Positive Almost Periodic Solution ◽  
Impulsive Perturbations

In order to obtain a more accurate description of the ecological system perturbed by human exploitation activities such as planting and harvesting, we need to consider the impulsive differential equations. Therefore, by applying the comparison theorem and the Lyapunov method of the impulsive differential equations, this paper gives some new sufficient conditions for the permanence and existence of a unique uniformly asymptotically stable positive almost periodic solution in a food chain system with almost periodic impulsive perturbations. The method used in this paper provides a possible method to study the permanence and existence of a unique uniformly asymptotically stable positive almost periodic solution of the models with impulsive perturbations in biological populations. Finally, an example and numerical simulations are given to illustrate that our results are feasible.

scholarly journals Solution of Some Impulsive Differential Equations via Coupled Fixed Point

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 501
Author(s):  
Ahmed Boudaoui ◽  
Khadidja Mebarki ◽  
Wasfi Shatanawi ◽  
Kamaleldin Abodayeh
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
System Of Differential Equations ◽  
Coupled Fixed Points

In this article, we employ the notion of coupled fixed points on a complete b-metric space endowed with a graph to give sufficient conditions to guarantee a solution of system of differential equations with impulse effects. We derive recisely some new coupled fixed point theorems under some conditions and then apply our results to achieve our goal.

scholarly journals Second-order impulsive differential systems with mixed and several delays

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shyam Sundar Santra ◽  
Apurba Ghosh ◽  
Omar Bazighifan ◽  
Khaled Mohamed Khedher ◽  
Taher A. Nofal
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Oscillation Theory ◽  
Second Order ◽  
Neutral Delay ◽  
Differential Systems ◽  
Impulsive Differential Systems ◽  
Several Delays ◽  
Necessary And Sufficient

AbstractIn this work, we present new necessary and sufficient conditions for the oscillation of a class of second-order neutral delay impulsive differential equations. Our oscillation results complement, simplify and improve recent results on oscillation theory of this type of nonlinear neutral impulsive differential equations that appear in the literature. An example is provided to illustrate the value of the main results.

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