Note on a Functional—Differential Inequality

2002 ◽  
pp. 21-24
Author(s):  
Bogdan Choczewski
Keyword(s):  
Differential Inequality ◽  
Functional Differential

scholarly journals Functional Differential Inequalities with Unbounded Delay

2005 ◽  
Vol 12 (2) ◽  
pp. 237-254
Author(s):  
Zdzisław Kamont ◽  
Adam Nadolski
Keyword(s):  
Differential Inequality ◽  
Continuous Dependence ◽  
Functional Differential Equations ◽  
Uniqueness Result ◽  
Classical Solutions ◽  
Differential Inequalities ◽  
Unbounded Delay ◽  
Several Variables ◽  
Functional Differential ◽  
Continuous Dependence Of Solutions

Abstract We prove that a function of several variables satisfying a functional differential inequality with unbounded delay can be estimated by a solution of a suitable initial problem for an ordinary functional differential equation. As a consequence of the comparison theorem we obtain a Perron-type uniqueness result and a result on continuous dependence of solutions on given functions for partial functional differential equations with unbounded delay. We consider classical solutions on the Haar pyramid.

On constant sign solutions (nonpositive) of certain functional differential inequality

2009 ◽  
Author(s):  
Zdeněk Opluštil ◽  
Alberto Cabada ◽  
Eduardo Liz ◽  
Juan J. Nieto
Keyword(s):  
Differential Inequality ◽  
Constant Sign ◽  
Constant Sign Solutions ◽  
Functional Differential

scholarly journals Stability Analysis of Impulsive Stochastic Functional Differential Equations with Delayed Impulses via Comparison Principle and Impulsive Delay Differential Inequality

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Pei Cheng ◽  
Fengqi Yao ◽  
Mingang Hua
Keyword(s):  
Comparison Principle ◽  
Differential Inequality ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Impulsive Delay ◽  
Functional Differential ◽  
Delay Differential ◽  
Delayed Impulses ◽  
Stochastic Functional ◽  
Delay Differential Inequality

The problem of stability for nonlinear impulsive stochastic functional differential equations with delayed impulses is addressed in this paper. Based on the comparison principle and an impulsive delay differential inequality, some exponential stability and asymptotical stability criteria are derived, which show that the system will be stable if the impulses’ frequency and amplitude are suitably related to the increase or decrease of the continuous stochastic flows. The obtained results complement ones from some recent works. Two examples are discussed to illustrate the effectiveness and advantages of our results.

scholarly journals Differential inequalities for hysteresis systems

1996 ◽  
Vol 9 (4) ◽  
pp. 459-468 ◽  
Author(s):  
Vladimir V. Chernorutskii ◽  
Mark A. Krasnosel'skii
Keyword(s):  
Differential Equations ◽  
State Space ◽  
Differential Inequality ◽  
Functional Differential Equations ◽  
The State ◽  
Differential Inequalities ◽  
Functional Differential

The theory of differential inequalities is extended to functional-differential equations with hysteresis nonlinearities. A key feature is the existence of a semiorder of the state space of nonlinearity and a special monotonicity of the righthand side of differential inequality.This article is dedicated to the memory of Roland L. Dobrushin.

scholarly journals A NEW GENERALIZATION OF THE HADDOCK CONJECTURE

2017 ◽  
Vol 22 (5) ◽  
pp. 634-642 ◽  
Author(s):  
Songlin Xiao
Keyword(s):  
Differential Equations ◽  
Differential Inequality ◽  
Functional Differential Equations ◽  
Time Varying ◽  
Neutral Functional Differential Equations ◽  
Inequality Techniques ◽  
Functional Differential ◽  
New Criteria ◽  
Asymptotic Constancy

In this paper, we establish some new criteria on the boundedness and asymptotic constancy of solutions for a class of scalar neutral functional differential equations with time-varying delays via differential inequality techniques. Our results are an improvement of existing ones and generalization of the Haddock conjecture.

Nonpositive solutions of one functional differential inequality

2009 ◽  
Vol 12 (4) ◽  
pp. 474-509 ◽  
Author(s):  
A. Lomtatidze ◽  
Z. Opluštil ◽  
J. Šremr
Keyword(s):  
Differential Inequality ◽  
Functional Differential

scholarly journals On the Oscillation of Conformable Impulsive Vector Partial Differential Equations

2020 ◽  
Vol 76 (1) ◽  
pp. 95-114
Author(s):  
George E. Chatzarakis ◽  
Kandhasamy Logaarasi ◽  
Thangaraj Raja ◽  
Vadivel Sadhasivam
Keyword(s):  
Differential Equations ◽  
Differential Inequality ◽  
Functional Differential Equations ◽  
Inner Product ◽  
One Dimensional ◽  
Inequality Technique ◽  
Impulsive Delay ◽  
Functional Differential ◽  
Delay Differential ◽  
Impulsive Differential Inequality

AbstractIn this paper, we study the oscillations of a class of conformable impulsive vector partial functional differential equations. For this class, our approach is to reduce the multi-dimensional oscillation problems to that of one dimensional impulsive delay differential inequalities by applying inner product reducing dimension method and an impulsive differential inequality technique. We provide an example to illustrate the effectiveness of our main results.

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