Results 41 to 50 of about 28,949 (123)

Lyapunov-type inequalities for nonlinear systems

Journal of Mathematical Analysis and Applications, 2007
The authors consider a nonlinear system of differential equations in the form \[ \begin{aligned} & x'(t) = \alpha _1 (t)x(t) + \beta _1 (t)\left| {u(t)} \right| ^{\gamma - 2}u(t), \\ & u'(t) = - \beta _2 (t)\left| {x(t)} \right| ^{\beta - 2}x(t) - \alpha _1 (t)u(t),\end{aligned} \tag{1} \] containing as special cases the well-known equations of Emden ...
Tiryaki, Aydin, Unal, Mehmet, ÇAKMAK, DEVRİM   +2 more
openaire   +3 more sources

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

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
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Exponential stability of stochastic Hopfield neural network with mixed multiple delays

AIMS Mathematics, 2021
This paper investigates the problem for exponential stability of stochastic Hopfield neural networks involving multiple discrete time-varying delays and multiple distributed time-varying delays.
Qinghua Zhou , Li Wan , Hongbo Fu, Qunjiao Zhang   +3 more
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Smale flows on $\mathbb{S}^2\times\mathbb{S}^1$

, 2014
In this paper, we use abstract Lyapunov graphs as a combinatorial tool to obtain a complete classification of Smale flows on $\mathbb{S}^2\times\mathbb{S}^1$.
de Rezende, Ketty A., Ledesma, Guido G. E., Neto, Oziride M.   +2 more
core   +1 more source

A Lyapunov-type inequality for a -Laplacian operator

Nonlinear Analysis: Theory, Methods & Applications, 2011
For an odd increasing function \(\psi\), a Lyapunov-type inequality for the \(\psi\)-Laplacian operator is proven. The proof is non-classical, since the Jensen, Cauchy-Schwarz or either Hölder inequalities are not used.
Sanchez, Justino, Vergara, Vicente
openaire   +6 more sources

LYAPUNOV TYPE INEQUALITY FOR DISCRETE FRACTIONAL BOUNDARY VALUE PROBLEM

South East Asian J. of Mathematics and Mathematical Sciences, 2023
In this paper we consider the discrete fractional boundary value problem. The Green’s function and it’s properties are used to find maximum value of function. With the help of maximum value of the function Lyapunov type inequality is obtain for this problem.
Abuj, Narayan G., Pachpatte, Deepak B.
openaire   +3 more sources

Investigation of a Lyapunov delta-type inequality with respect to a discrete fractional Green’s function

Scientific Reports
This article considers a Lyapunov delta-type inequality with Green’s functions including fractional falling functions. We define a fractional difference problem of Riemann-Liouville type with a fractional boundary condition and, using the Green’s ...
Pshtiwan Othman Mohammed, Meraa Arab
doaj   +1 more source

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

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