impulsive delay differential equations
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2021 ◽  
Vol 6 (8) ◽  
pp. 8149-8172
Author(s):  
Hua Wang ◽  
◽  
Tahir Ullah Khan ◽  
Muhammad Adil Khan ◽  
Sajid Iqbal ◽  
...  

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1802
Author(s):  
Ali Fuat Yeniçerioğlu ◽  
Vildan Yazıcı ◽  
Cüneyt Yazıcı

We study first order linear impulsive delay differential equations with periodic coefficients and constant delays. This study presents some new results on the asymptotic behavior and stability. Thus, a proper real root was used for a representative characteristic equation. Applications to special cases, such as linear impulsive delay differential equations with constant coefficients, were also presented. In this study, we gave three different cases (stable, asymptotic stable and unstable) in one example. The findings suggest that an equation that is in a way that characteristic equation plays a crucial role in establishing the results in this study.


Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 523 ◽  
Author(s):  
Mostafa Bachar

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 ) .


2018 ◽  
Vol 71 (1) ◽  
pp. 65-70
Author(s):  
Alexander Domoshnitsky ◽  
Vladimir Raichik

Abstract Wronskian is one of the classical objects in the theory of ordinary differential equations. Properties of Wronskian lead to important conclusions on behaviour of solutions of delay equations. For instance, non-vanishing Wronskian ensures validity of the Sturm separation theorem (between two adjacent zeros of any solution there is one and only one zero of every other nontrivial linearly independent solution) for delay equations. We propose the Sturm separation theorem in the case of impulsive delay differential equations and obtain assertions about its validity.


2018 ◽  
Vol 7 (3) ◽  
pp. 247-251
Author(s):  
Palwinder Singh ◽  
Sanjay K. Srivastava ◽  
Kanwalpreet Kaur

Abstract In present study, some sufficient conditions for the exponential stability of impulsive delay differential equations are obtained by introducing weight function in the norm and applying the concept of Lyapunov functions and Razumikhin techniques. The function ψ plays the role of weight and hence increases the rate of convergence towards stability. The obtained results are demonstrated with examples.


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