On the multiple zeros of a real analytic function with applications to the averaging theory of differential equations

摘要

In this work we consider real analytic functions d(z, lambda, epsilon), where d : Omega x R-p x I - Omega, Omega is a bounded open subset of R, I subset of R is an interval containing the origin, lambda is an element of R-p are parameters, and epsilon is a small parameter. We study the branching of the zero-set of d(z, lambda, epsilon) at multiple points when the parameter epsilon varies.