Department of Mathematics and Statistics, San Diego State University

Seminars on Differential and Difference Equations,

and Dynamical Systems

Method of averaging in investigating asymptotic behavior of solutions of linear difference equations.

Alex Bourd, Qualcomm Inc.

I will start with reviewing a few classical results on the asymptotic representation of solutions of difference equations, such as Theorems of Poincare and Perron, and difference analogs of The Asymptotic Theorem of Levinson obtained by Rapoport and Benzaid-Lutz. I will then show how to apply the method of averaging (developed by Bogolyubov for systems of ODE) for constructing asymptotic representations of solutions for some new classes of systems of linear difference equations.

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