Results 21 to 30 of about 3,016 (203)

The eigenvalue product bounds of the Lyapunov matrix differential equation and the stability of a class of time-varying nonlinear system

Journal of Inequalities and Applications, 2019
The Lyapunov matrix differential equation plays an important role in many scientific and engineering fields. In this paper, we first give a class relation between the eigenvalue of functional matrix derivative and the derivative of functional matrix ...
Jianzhou Liu, Juan Zhang, Hao Huang
doaj   +1 more source

On the Lyapunov Type Inequality

Russian Mathematics, 2020
The author's main result concernes an estimate on the zeros of the solutions to a linear equation of the type \[ x''+p(t)x'(t)+q(t)x=0. \] When \(p(t)\) is identically equal to zero, Lyapunov provided the following result: if \(x(t)\) is a solution such that \(x(a)=x(b)=0\) and \(x(t)\ne0\) for every \(t\in(a,b)\), then \[ \int_a^b|q(t)|\,dt\ge\frac{4}{
openaire   +4 more sources

Dynamic multi‐objective optimisation of complex networks based on evolutionary computation

IET Networks, EarlyView., 2022
Abstract As the problems concerning the number of information to be optimised is increasing, the optimisation level is getting higher, the target information is more diversified, and the algorithms are becoming more complex; the traditional algorithms such as particle swarm and differential evolution are far from being able to deal with this situation ...
Linfeng Huang
wiley   +1 more source

A Lyapunov-Type Inequality for a Laplacian System on a Rectangular Domain with Zero Dirichlet Boundary Conditions

Mathematics, 2019
We consider a coupled system of partial differential equations involving Laplacian operator, on a rectangular domain with zero Dirichlet boundary conditions. A Lyapunov-type inequality related to this problem is derived.
Mohamed Jleli, Bessem Samet
doaj   +1 more source

LYAPUNOV-TYPE INEQUALITY FOR EXTREMAL PUCCI’S EQUATIONS [PDF]

Journal of the Australian Mathematical Society, 2020
AbstractIn this article, we establish a Lyapunov-type inequality for the following extremal Pucci’s equation:$$\begin{eqnarray}\left\{\begin{array}{@{}ll@{}}{\mathcal{M}}_{\unicode[STIX]{x1D706},\unicode[STIX]{x1D6EC}}^{+}(D^{2}u)+b(x)|Du|+a(x)u=0 & \text{in}~\unicode[STIX]{x1D6FA},\\ u=0 & \text{on}~\unicode[STIX]{x2202}\unicode[STIX]{x1D6FA},\
J. TYAGI, R. B. VERMA
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A Lyapunov-Type Inequality for a Fractional Differential Equation under a Robin Boundary Condition

Journal of Function Spaces, 2015
We establish a new Lyapunov-type inequality for a class of fractional differential equations under Robin boundary conditions. The obtained inequality is used to obtain an interval where a linear combination of certain Mittag-Leffler functions has no real
Mohamed Jleli, Lakhdar Ragoub, Bessem Samet   +2 more
doaj   +1 more source

$H_\infty$ Synchronization for Uncertain Time-Delay Chaotic Systems With One-Sided Lipschitz Nonlinearity

IEEE Access, 2018
This paper addresses H∞ synchronization for uncertain chaotic systems with one-sided Lipschitz nonlinearity under the output and intrinsic state delays.
Zhanshan Zhao, Fei Lv, Jing Zhang, Yanan Du   +3 more
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Wirtinger-Type Inequality and the Stability Analysis of Delayed Lur'e System

Discrete Dynamics in Nature and Society, 2013
This paper proposes a new delay-depended stability criterion for a class of delayed Lur'e systems with sector and slope restricted nonlinear perturbation.
Zixin Liu, Jian Yu, Daoyun Xu, Dingtao Peng   +3 more
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Lyapunov-type inequalities for nonlinear fractional differential equations and systems involving Caputo-type fractional derivatives

Journal of Inequalities and Applications, 2019
A Lyapunov-type inequality is derived for a nonlinear fractional boundary value problem involving Caputo-type fractional derivative. The obtained inequality provides a necessary condition for the existence of nontrivial solutions to the considered ...
Mohamed Jleli, Bessem Samet, Yong Zhou
doaj   +1 more source

Lyapunov-type inequalities for sequential fractional boundary value problems using Hilfer’s fractional derivative

Journal of Inequalities and Applications, 2019
This paper is devoted to studying the Lyapunov-type inequality for sequential Hilfer fractional boundary value problems. We first provide some properties of Hilfer fractional derivative, and then establish Lyapunov-type inequalities for a sequential ...
Wei Zhang, Wenbin Liu
doaj   +1 more source