Uniformly continuous solutions of difference equations with continuous time

Asymptotic Behavior of Solutions of a Scalar Delay Difference Equations with Continuous Time

Huang, Yu and Dai in [4], [5] presented conditions when every solution of discrete difference equation xn−xn−1 = −F (xn)+F (xn−k) is bounded and tends to a constant, where k ∈ N, F is a continuous, increasing real function. Similar problems for differential equation x′(t) = β(t)[x(t)−x(t− τ(t))], where τ and β are positive continuous real functions, was investigated in papers by Atkinson and Ha...

About Lyapunov functionals construction for difference equations with continuous time

Stability investigation of hereditary systems is connected often with construction of Lyapunov functionals. One general method of Lyapunov functionals construction was proposed and developed in [1-9] both for differential equations with aftereffect and for difference equations with discrete time. Here, some modification of Lyapunov-type stability theorem is proposed, which allows one to use thi...

Continuous Symmetries of Difference Equations

Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much more recent program: the use of Lie groups to study difference equations. We show that the mismatch between continuous symmetries and discrete equations can be resolved in at least two manners. One is to use generalize...

Continuous Solutions of Linear Equations

On continuous solutions of a class of systems of nonlinear functional difference equations with deviating argument

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t Bounded continuous solutions on R þ of a class of systems of nonlinear functional difference equations with ...