On a differential inequality

Analysis ◽  
2008 ◽  
Vol 28 (3) ◽  
Author(s):  
Richard Fournier
Keyword(s):  
Differential Inequality ◽  
Extremal Functions ◽  
Differential Inequalities

We identify the extremal functions for a class of differential inequalities first introduced by Sanford S. Miller and P. T. Mocanu in 1978.

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.

scholarly journals Starlikeness of meromorphic functions involving certain differential inequalities

2021 ◽  
Vol 5 (1) ◽  
pp. 64-68
Author(s):  
Kuldeep Kaur Shergill ◽  
◽  
Sukhwinder Singh Billing ◽  
Keyword(s):  
Unit Disk ◽  
Differential Inequality ◽  
Meromorphic Functions ◽  
Differential Inequalities ◽  
Bazilevic Functions ◽  
New Criteria

In the present paper, we define a class of non-Bazilevic functions in punctured unit disk and study a differential inequality to obtain certain new criteria for starlikeness of meromorphic functions.

scholarly journals Solvability of a New q-Differential Equation Related to q-Differential Inequality of a Special Type of Analytic Functions

2021 ◽  
Vol 5 (4) ◽  
pp. 228
Author(s):  
Ibtisam Aldawish ◽  
Rabha W. Ibrahim
Keyword(s):  
Differential Equation ◽  
Differential Operator ◽  
Analytic Functions ◽  
Differential Inequality ◽  
Laguerre Polynomial ◽  
Analytic Solutions ◽  
Confluent Hypergeometric Function ◽  
Differential Inequalities ◽  
Quantum Calculus

The current study acts on the notion of quantum calculus together with a symmetric differential operator joining a special class of meromorphic multivalent functions in the puncher unit disk. We formulate a quantum symmetric differential operator and employ it to investigate the geometric properties of a class of meromorphic multivalent functions. We illustrate a set of differential inequalities based on the theory of subordination and superordination. In this real case study, we found the analytic solutions of q-differential equations. We indicate that the solutions are given in terms of confluent hypergeometric function of the second type and Laguerre polynomial.

scholarly journals An integro-differential inequality related to the smallest positive eigenvalue of p(x)-Laplacian Dirichlet problem

2016 ◽  
Vol 15 (1) ◽  
pp. 27-36
Author(s):  
Damian Wiśniewski ◽  
Mariusz Bodzioch
Keyword(s):  
Dirichlet Problem ◽  
Eigenvalue Problem ◽  
Unit Sphere ◽  
Differential Inequality ◽  
Beltrami Operator ◽  
Positive Eigenvalue ◽  
Differential Inequalities

AbstractWe consider the eigenvalue problem for the p(x)-Laplace-Beltrami operator on the unit sphere. We prove same integro-differential inequalities related to the smallest positive eigenvalue of this problem.

scholarly journals Necessary and sufficient conditions for oscillations of delay differential inequalities

1989 ◽  
Vol 39 (2) ◽  
pp. 161-165
Author(s):  
Jurang Yan
Keyword(s):  
Differential Inequality ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Differential Inequalities ◽  
Necessary And Sufficient Condition ◽  
First Order ◽  
Linear Delay ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Delay Differential Inequality

A necessary and sufficient condition is obtained for a first order linear delay differential inequality to be oscillatory. Our main result improves and extends some known results.

Two-sided estimates for solutions of boundary value problems for implicit differential equations

2021 ◽  
pp. 216-220
Author(s):  
Sarra Benarab
Keyword(s):  
Differential Equations ◽  
Differential Inequality ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Control Problems ◽  
Differential Inequalities ◽  
System Of Differential Equations ◽  
Estimates Of Solutions ◽  
Ordered Space ◽  
Special Order

We consider a two-point (including periodic) boundary value problem for the following system of differential equations that are not resolved with respect to the derivative of the desired function: f_i (t,x,x ̇,(x_i ) ̇ )=0,i= (1,n) ̅. Here, for any i= (1,n) ̅ the function f_i:[0,1]×R^n×R^n×R→R is measurable in the first argument, continuous in the last argument, right-continuous, and satisfies the special condition of monotonicity in each component of the second and third arguments. Assertions about the existence and two-sided estimates of solutions (of the type of Chaplygin’s theorem on differential inequality) are obtained. Conditions for the existence of the largest and the smallest (with respect to a special order) solution are also obtained. The study is based on results on abstract equations with mappings acting from a partially ordered space to an arbitrary set (see [S. Benarab, Z.T. Zhukovskaya, E.S. Zhukovskiy, S.E. Zhukovskiy. On functional and differential inequalities and their applications to control problems // Differential Equations, 2020, 56:11, 1440–1451]).

scholarly journals Further results on differential inequality of a class of second order neutral type

2004 ◽  
Vol 35 (1) ◽  
pp. 43-52 ◽  
Author(s):  
Peiguang Wang ◽  
Yonghong Wu
Keyword(s):  
Positive Solutions ◽  
Differential Inequality ◽  
Neutral Type ◽  
Second Order ◽  
Differential Inequalities ◽  
Deviating Arguments ◽  
Distributed Deviating Arguments ◽  
Existing Result

In this paper, we develop several new results related to the nonexistence criteria for eventually positive solutions of a class of second order neutral differential inequalities with distributed deviating arguments. The work generalizes various existing result.

scholarly journals On the absence of global solutions to two-times-fractional differential inequalities involving Hadamard-Caputo and Caputo fractional derivatives

2022 ◽  
Vol 7 (4) ◽  
pp. 5830-5843
Author(s):  
Ibtehal Alazman ◽  
◽  
Mohamed Jleli ◽  
Bessem Samet ◽  
Keyword(s):  
Global Solution ◽  
Differential Inequality ◽  
Fractional Derivatives ◽  
Singular Potential ◽  
Global Solutions ◽  
Differential Inequalities ◽  
Caputo Fractional Derivatives ◽  
Potential Term ◽  
Fractional Differential ◽  
Derivatives Of

<abstract><p>In this paper, we consider a two-times nonlinear fractional differential inequality involving both Hadamard-Caputo and Caputo fractional derivatives of different orders, with a singular potential term. We obtain sufficient criteria depending on the parameters of the problem, for which a global solution does not exist. Some examples are provided to support our main results.</p></abstract>

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 On Removable Singularities of Solutions of Higher-Order Differential Inequalities

2020 ◽  
Vol 20 (2) ◽  
pp. 385-397
Author(s):  
A. A. Kon’kov ◽  
A. E. Shishkov
Keyword(s):  
Unit Ball ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Removable Singularity ◽  
Higher Order ◽  
Differential Inequalities ◽  
Removable Singularities

AbstractWe obtain sufficient conditions for solutions of the mth-order differential inequality\sum_{|\alpha|=m}\partial^{\alpha}a_{\alpha}(x,u)\geq f(x)g(|u|)\quad\text{in % }B_{1}\setminus\{0\}to have a removable singularity at zero, where {a_{\alpha}}, f, and g are some functions, and {B_{1}=\{x:|x|<1\}} is a unit ball in {{\mathbb{R}}^{n}}. We show in some examples the sharpness of these conditions.

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