will talk on
Formulas of Bendixson and Alekseev
for Difference Equations.
A well-known formula of Bendixson states that solutions of first order
differential equations, as functions of their initial conditions, satisfy
a certain partial differential equation. A consequence is Alekseev's
nonlinear variation of parameters formula. In this talk we prove
corresponding results for difference equations. To achieve this, we make use
of the recently introduced concept of alpha derivatives rather than of
differences or usual derivatives. This technique allows us to also
offer generalizations of our results to alpha dynamic equations, which
include among others ordinary differential and difference equations.