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 Exponential Stability of Impulsive Delay Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
G. L. Zhang ◽  
M. H. Song ◽  
M. Z. Liu
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Euler Method ◽  
Exponentially Stable ◽  
Impulsive Delay Differential Equations ◽  
Numerical Process ◽  
Impulsive Delay ◽  
Delay Differential

The main objective of this paper is to further investigate the exponential stability of a class of impulsive delay differential equations. Several new criteria for the exponential stability are analytically established based on Razumikhin techniques. Some sufficient conditions, under which a class of linear impulsive delay differential equations are exponentially stable, are also given. An Euler method is applied to this kind of equations and it is shown that the exponential stability is preserved by the numerical process.

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