Variational Lyapunov Method for Difference Equations

摘要

In this article we consider the difference equation △y(n) = f(n, y), y(n{sub}0) = x{sub}0, (A), with a smoothness condition on f with respect to y. We study the dependence of solutions of (A) on initial data and then obtain a discrete analog of Alekseev's variation of parameters formula. In addition, we develop a Variational Lyapunov Method (VLM) and use it to study the stability properties of difference equations.