Kinematical similarity and exponential dichotomy of linear abstract impulsive differential equations

1994 ◽  
Vol 33 (2) ◽  
pp. 487-497 ◽  
Author(s):  
D. D. Bainov ◽  
S. I. Kostadinov ◽  
A. D. Myshkis
Keyword(s):  
Differential Equations ◽  
Exponential Dichotomy ◽  
Impulsive Differential Equations

Existence of exponential dichotomy of a class of impulsive differential equations

1995 ◽  
Vol 34 (1) ◽  
pp. 135-143 ◽  
Author(s):  
D. D. Bainov ◽  
S. I. Kostadinov ◽  
Nguyen Van Minh ◽  
P. P. Zabreiko
Keyword(s):  
Differential Equations ◽  
Exponential Dichotomy ◽  
Impulsive Differential Equations

scholarly journals Linearization of Nonautonomous Impulsive System with Nonuniform Exponential Dichotomy

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yongfei Gao ◽  
Yonghui Xia ◽  
Xiaoqing Yuan ◽  
P. J. Y. Wong
Keyword(s):  
Linear System ◽  
Differential Equations ◽  
Exponential Dichotomy ◽  
Impulsive Differential Equations ◽  
Impulsive System ◽  
Topological Conjugacy ◽  
Equivalent Function ◽  
Nonlinear Impulsive System ◽  
Nonuniform Exponential Dichotomy

This paper gives a version of Hartman-Grobman theorem for the impulsive differential equations. We assume that the linear impulsive system has a nonuniform exponential dichotomy. Under some suitable conditions, we proved that the nonlinear impulsive system is topologically conjugated to its linear system. Indeed, we do construct the topologically equivalent function (the transformation). Moreover, the method to prove the topological conjugacy is quite different from those in previous works (e.g., see Barreira and Valls, 2006).

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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