On an inequality of Kolmogorov type for a second-order difference expression.
On approximation of the solutions of delay differential equations by using piecewise constant arguments.
On asymptotics of discrete Mittag-Leffler function
The (modified) two-parametric Mittag-Leffler function plays an essential role in solving the so-called fractional differential equations. Its asymptotics is known (at least for a subset of its domain and special choices of the parameters). The aim of the paper is to introduce a discrete analogue of this function as a solution of a certain two-term linear fractional difference equation (involving both the Riemann-Liouville as well as the Caputo fractional -difference operators) and describe its...
On boundary value problems for second-order discrete inclusions.
On boundedness of solutions of the difference equation for .
On boundedness of the solutions of the difference equation .
On Cauchy differences of all orders.
On certain comparison theorems for half-linear dynamic equations on time scales.
On dichotomous behavior of variational difference equations and applications.
On difference equation with generalized dilation.
On difference equations and discrete systems
On difference linear periodic systems. I. Homogeneous case
The paper deals with the reduction of a linear homogeneous periodic system in differences (recurrence relations) to another linear homogeneous system with constant coefficients. This makes it possible to study the existence and properties of periodic solutions, the asymptotic behavior, and to obtain all solutions in closed form.
On difference linear periodic systems II. Non-homogeneous case
This work deals with the reduction of a linear nonhomogeneous periodic system in differences (recurrence relations) to another linear non-homogeneous system with constant coefficients and an independent term. This makes it possible to study the existence and properties of periodic solutions, the asymptotic behavior and to obtain all solutions in closed form.
On discrete analogues of nonlinear implicit differential equations.
On exponential dichotomy of variational difference equations.
On Exponential Stability of Volterra Difference Equations with Infinite Delay
General nonlinear Volterra difference equations with infinite delay are considered. A new explicit criterion for global exponential stability is given. Furthermore, we present a stability bound for equations subject to nonlinear perturbations. Two examples are given to illustrate the results obtained.
On generalized difference equations
In this paper linear difference equations with several independent variables are considered, whose solutions are functions defined on sets of -dimensional vectors with integer coordinates. These equations could be called partial difference equations. Existence and uniqueness theorems for these equations are formulated and proved, and interconnections of such results with the theory of linear multidimensional digital systems are investigated. Numerous examples show essential differences of the results...
On global attractivity of a class of nonautonomous difference equations.
On global exponential stability of discrete-time Hopfield neural networks with variable delays.
On global periodicity of a class of difference equations.