Results 31 to 40 of about 25,247 (223)

A generalized Lyapunov-type inequality in the frame of conformable derivatives

Advances in Difference Equations, 2017
We prove a generalized Lyapunov-type inequality for a conformable boundary value problem (BVP) of order α ∈ ( 1 , 2 ] $\alpha \in (1,2]$ . Indeed, it is shown that if the boundary value problem ( T α c x ) ( t ) + r ( t ) x ( t ) = 0 , t ∈ ( c , d ) , x (
Thabet Abdeljawad, Jehad Alzabut, Fahd Jarad   +2 more
doaj   +1 more source

On Lyapunov-type inequality for a class of nonlinear systems [PDF]

Mathematical Inequalities & Applications, 2013
In this paper, we will try to find a new Lyapunov-type inequality for a class of nonlinear systems, special cases of which contain some well-known Hamiltonian system, EmdenFowler, half-linear and linear differential equations of second order. Our result extends the Lyapunov-type inequality given in [X.
openaire   +2 more sources

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
doaj   +1 more source

Lyapunov-type inequalities for generalized one-dimensional Minkowski-curvature problems

Journal of Inequalities and Applications, 2020
In this paper, we consider some types of scalar equations and systems of generalized one-dimensional Minkowski-curvature problems. Using an inequality technique, we establish several new Lyapunov-type inequalities for the problems considered. Our results
Haidong Liu
doaj   +1 more source

The best constant of Sobolev inequality corresponding to anti-periodic boundary value problem

Electronic Journal of Qualitative Theory of Differential Equations, 2014
In this paper we establish the best constant of $\mathcal{L}^{p}$ Sobolev inequality for a function with anti-periodic boundary conditions. The best constant is expressed by $\mathcal{L}^q$ norm of $(M-1)$-th order Euler polynomial.
Jozef Kiseľák
doaj   +1 more source

Existence and uniqueness of mild solutions for a fractional differential equation under Sturm-Liouville boundary conditions when the data function is of Lipschitzian type

Demonstratio Mathematica, 2020
In this article, we present a sufficient condition about the length of the interval for the existence and uniqueness of mild solutions to a fractional boundary value problem with Sturm-Liouville boundary conditions when the data function is of ...
Harjani Jackie, López Belen, Sadarangani Kishin   +2 more
doaj   +1 more source

Lyapunov-type inequalities for third order nonlinear equations

Differential Equations & Applications, 2022
We derive Lyapunov-type inequalities for general third order nonlinear equations involving multiple $ψ$-Laplacian operators of the form \begin{equation*} (ψ_{2}((ψ_{1}(u'))'))' + q(x)f(u) = 0, \end{equation*} where $ψ_{2}$ and $ψ_{1}$ are odd, increasing functions, $ψ_{2}$ is super-multiplicative, $ψ_{1}$ is sub-multiplicative, and $\frac{1}{ψ_{1}}$ is
Behrens, Brian, Dhar, Sougata
openaire   +3 more sources

Arbitrary Order Fractional Difference Operators with Discrete Exponential Kernels and Applications

Discrete Dynamics in Nature and Society, 2017
Recently, Abdeljawad and Baleanu have formulated and studied the discrete versions of the fractional operators of order ...
Thabet Abdeljawad, Qasem M. Al-Mdallal, Mohamed A. Hajji   +2 more
doaj   +1 more source

DRIVE‐SAFE: Data‐Driven Robustness and Informed Validation for Evolving Specifications via Formal Evaluation

Advanced Robotics Research, EarlyView.
DRIVE‐SAFE evaluates learning‐based, black‐box autonomous driving policies against evolving temporal safety requirements using Signal Temporal Logic robustness metrics. It aggregates distributional robustness measures with domain‐informed weights to guide iterative retraining.
Kristy Sakano, Jianyu An, Dinesh Manocha, Huan Xu   +3 more
wiley   +1 more source

“It Is Much Safer to Be Sparse than Connected”: Safe Control of Robotic Swarm Density Dynamics with PDE Optimization with State Constraints

Advanced Intelligent Systems, EarlyView.
This paper proposes a novel control framework to ensure safety of a robotic swarm. A feedback optimization controller is capable of driving the swarm toward a target density while keeping risk‐zone exposure below a safety threshold. Theory and experiments show how safety is more effectively achieved for sparsely connected swarms.
Longchen Niu, Gennaro Notomista
wiley   +1 more source