scholarly journals Practical Stability with Respect to h-Manifolds for Impulsive Control Functional Differential Equations with Variable Impulsive Perturbations

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 656 ◽  
Author(s):  
Gani Stamov ◽  
Ivanka Stamova ◽  
Xiaodi Li ◽  
Ekaterina Gospodinova
Keyword(s):  
Differential Equations ◽  
Impulsive Control ◽  
Functional Differential Equations ◽  
Cellular Neural Network ◽  
Continuous Functions ◽  
Practical Stability ◽  
Piecewise Continuous ◽  
Impulsive Perturbations ◽  
Functional Differential ◽  
Control Functional

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.

scholarly journals BOUNDEDNESS OF IMPULSIVE FUNCTIONAL DIFFERENTIAL EQUATIONS WITH VARIABLE IMPULSIVE PERTURBATIONS

2008 ◽  
Vol 77 (2) ◽  
pp. 331-345 ◽  
Author(s):  
I. M. Stamova
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Boundedness Of Solutions ◽  
Initial Value ◽  
Razumikhin Technique ◽  
Piecewise Continuous ◽  
Impulsive Perturbations ◽  
Functional Differential

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.

scholarly journals Stability of the solutions of impulsive functional-differential equations by Lyapunov's direct method

2001 ◽  
Vol 43 (2) ◽  
pp. 269-278 ◽  
Author(s):  
D. D. Bainov ◽  
I. M. Stamova
Keyword(s):  
Differential Equations ◽  
Lyapunov Functions ◽  
Direct Method ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Continuous Functions ◽  
Piecewise Continuous ◽  
Functional Differential ◽  
The Stability

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.

Almost Periodicity and Lyapunov's Functions for Impulsive Functional Differential Equations with Infinite Delays

2010 ◽  
Vol 53 (2) ◽  
pp. 367-377 ◽  
Author(s):  
Gani Tr. Stamov
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Infinite Delay ◽  
Functional Differential Equations ◽  
Continuous Functions ◽  
Differential Inequalities ◽  
Almost Periodic ◽  
Infinite Delays ◽  
Piecewise Continuous ◽  
Functional Differential

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.

Uniform practical stability in terms of two measures with effect of delay at the time of impulses

2016 ◽  
Vol 0 (0) ◽  
Author(s):  
Palwinder Singh ◽  
Sanjay K. Srivastava ◽  
Kanwalpreet Kaur
Keyword(s):  
Differential Equations ◽  
Lyapunov Functions ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Practical Stability ◽  
Two Measures ◽  
Piecewise Continuous ◽  
Functional Differential

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.

Periodic solutions to functional differential equations

1985 ◽  
Vol 101 (3-4) ◽  
pp. 253-271 ◽  
Author(s):  
O. A. Arino ◽  
T. A. Burton ◽  
J. R. Haddock
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Uniform Boundedness ◽  
Continuous Functions ◽  
Ultimate Boundedness ◽  
Space Of Continuous Functions ◽  
Uniform Ultimate Boundedness ◽  
Functional Differential ◽  
Image Position

SynopsisWe consider a system of functional differential equationswhere G: R × B → Rn is T periodic in t and B is a certain phase space of continuous functions that map (−∞, 0[ into Rn. The concepts of B-uniform boundedness and B-uniform ultimate boundedness are introduced, and sufficient conditions are given for the existence of a T-periodic solution to (1.1). Several examples are given to illustrate the main theorem.

On the existence of periodic solutions for autonomous retarded functional differential equations on R2

1986 ◽  
Vol 102 (3-4) ◽  
pp. 259-262 ◽  
Author(s):  
J. G. Dos Reis ◽  
R. L. S. Baroni
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Continuous Functions ◽  
Retarded Functional Differential Equations ◽  
Existence Of Periodic Solutions ◽  
Functional Differential

SynopsisLet Ca be the set of all the continuous functions from the interval [−r, 0] on the sphere of radius a, on the plane. We prove, under certains conditions, that a retarded autonomous differential equation that leaves Ca invariant has a non-constant periodic solution.

scholarly journals The Kneser property for abstract retarded functional differential equations with infinite delay

2003 ◽  
Vol 2003 (26) ◽  
pp. 1645-1661 ◽  
Author(s):  
Hernán R. Henríquez
Keyword(s):  
Differential Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Continuous Functions ◽  
Space Of Continuous Functions ◽  
First Order ◽  
Retarded Functional Differential Equations ◽  
Functional Differential

We establish existence of mild solutions for a class of semilinear first-order abstract retarded functional differential equations (ARFDEs) with infinite delay and we prove that the set consisting of mild solutions for this problem is connected in the space of continuous functions.

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