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 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 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.

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.

Bounded solutions of functional differential equations of the neutral type with infinite delays

1982 ◽  
Vol 93 (1-2) ◽  
pp. 33-39 ◽  
Author(s):  
V. G. Angelov ◽  
D. D. Bainov
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Existence And Uniqueness ◽  
Functional Differential Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Bounded Solutions ◽  
Initial Value ◽  
Infinite Delays ◽  
Functional Differential

SynopsisIn this paper the authors obtain sufficient conditions for the existence and uniqueness of the initial value problem of functional differential equations of neutral type with infinite delays, making use of some earlier results of the present authors.

scholarly journals Stability and boundedness to certain differential equations of fourth order with multiple delays

Filomat ◽  
2014 ◽  
Vol 28 (5) ◽  
pp. 1049-1058 ◽  
Author(s):  
Erdal Korkmaz ◽  
Cemil Tunc
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Fourth Order ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Multiple Delays ◽  
Boundedness Of Solutions ◽  
Functional Differential ◽  
The Stability

In this paper, we give sufficient conditions to guarantee the asymptotic stability and boundedness of solutions to a kind of fourth-order functional differential equations with multiple delays. By using the Lyapunov-Krasovskii functional approach, we establish two new results on the stability and boundedness of solutions, which include and improve some related results in the literature.

On a boundary value problem on an infinite interval for nonlinear functional differential equations

2017 ◽  
Vol 24 (2) ◽  
pp. 217-225 ◽  
Author(s):  
Ivan Kiguradze ◽  
Zaza Sokhadze
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Volterra Operator ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Infinite Interval ◽  
Nonlinear Functional ◽  
Functional Differential

AbstractSufficient conditions are found for the solvability of the following boundary value problem:u^{(n)}(t)=f(u)(t),\qquad u^{(i-1)}(0)=\varphi_{i}(u^{(n-1)}(0))\quad(i=1,% \dots,n-1),\qquad\liminf_{t\to+\infty}\lvert u^{(n-2)}(t)|<+\infty,where {f\colon C^{n-1}(\mathbb{R}_{+})\to L_{\mathrm{loc}}(\mathbb{R}_{+})} is a continuous Volterra operator, and {\varphi_{i}\colon\mathbb{R}\to\mathbb{R}} ({i=1,\dots,n}) are continuous functions.

scholarly journals Stability of functional differential equations of Volterra type

1984 ◽  
Vol 29 (1) ◽  
pp. 93-100
Author(s):  
M. Rama Mohana Rao ◽  
P. Srinivas
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Volterra Type ◽  
Stability Properties ◽  
Razumikhin Technique ◽  
Functional Differential

The Liapunov-Razumikhin technique has been employed to study Lp stability properties of solutions of functional differential equations of delay type where the delay becomes unbounded as t ↠ +∞. These results have been applied to investigate sufficient conditions for L2-stability of Volterra integro-differentlal equations.

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.

scholarly journals Lipschitz stability of impulsive functional-differential equations

2001 ◽  
Vol 42 (4) ◽  
pp. 504-514 ◽  
Author(s):  
D. D. Bainov ◽  
I. M. Stamova
Keyword(s):  
Population Dynamics ◽  
Differential Equations ◽  
Initial Value Problem ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Lipschitz Stability ◽  
Initial Value ◽  
Functional Differential

AbstractAn initial value problem is considered for impulsive functional-differential equations. The impulses occur at fixed moments of time. Sufficient conditions are found for Lipschitz stability of the zero solution of these equations. An application in impulsive population dynamics is also discussed.

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.

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