Functional Differential Equations with Piecewise Continuous Argument

1993 ◽  
Author(s):  
Gangaram S. Ladde ◽  
Joseph Wiener
Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 656 ◽  
Author(s):  
Gani Stamov ◽  
Ivanka Stamova ◽  
Xiaodi Li ◽  
Ekaterina Gospodinova

The present paper is devoted to the problems of practical stability with respect to h-manifolds for impulsive control differential equations with variable impulsive perturbations. We will consider these problems in light of the Lyapunov–Razumikhin method of piecewise continuous functions. The new results are applied to an impulsive control cellular neural network model with variable impulsive perturbations.


2008 ◽  
Vol 77 (2) ◽  
pp. 331-345 ◽  
Author(s):  
I. M. Stamova

AbstractIn the present paper an initial value problem for impulsive functional differential equations with variable impulsive perturbations is considered. By means of piecewise continuous functions coupled with the Razumikhin technique, sufficient conditions for boundedness of solutions of such equations are found.


2001 ◽  
Vol 43 (2) ◽  
pp. 269-278 ◽  
Author(s):  
D. D. Bainov ◽  
I. M. Stamova

AbstractWe consider the stability of the zero solution of a system of impulsive functional-differential equations. By means of piecewise continuous functions, which are generalizations of classical Lyapunov functions, and using a technique due to Razumikhin, sufficient conditions are found for stability, uniform stability and asymptotical stability of the zero solution of these equations. Applications to impulsive population dynamics are also discussed.


2010 ◽  
Vol 53 (2) ◽  
pp. 367-377 ◽  
Author(s):  
Gani Tr. Stamov

AbstractThis paper studies the existence and uniqueness of almost periodic solutions of nonlinear impulsive functional differential equations with infinite delay. The results obtained are based on the Lyapunov–Razumikhin method and on differential inequalities for piecewise continuous functions.


2016 ◽  
Vol 0 (0) ◽  
Author(s):  
Palwinder Singh ◽  
Sanjay K. Srivastava ◽  
Kanwalpreet Kaur

AbstractIn this paper, some sufficient conditions for uniform practical stability of impulsive functional differential equations in terms of two measures with effect of delay at the time of impulses are obtained by using piecewise continuous Lyapunov functions and Razumikhin techniques. The application of obtained result is illustrated with an example.


2007 ◽  
Vol 7 (1) ◽  
pp. 68-82
Author(s):  
K. Kropielnicka

AbstractA general class of implicit difference methods for nonlinear parabolic functional differential equations with initial boundary conditions of the Neumann type is constructed. Convergence results are proved by means of consistency and stability arguments. It is assumed that given functions satisfy nonlinear estimates of Perron type with respect to functional variables. Differential equations with deviated variables and differential integral problems can be obtained from a general model by specializing given operators. The results are illustrated by numerical examples.


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