Periodic and almost periodic solutions of strongly non-linear impulsive systems

The problem of the existence and stability of periodic and almost periodic solutions of strongly non-linear impulsive systems is investigated. The Poincaré method 1] is justified for the case of an isolated generating solution. A dynamical system consisting of a bead on a vibrating surface is considered as an example.

The small parameter method for investigating systems with discontinuous solutions was previously applied 2, 3] to the case when the periodic solution is non-isolated.

A method is used below for reducing the investigation of a system of equations with impulsive actions on surfaces to equations with fixed moments of inpulsive action.