Construction of Asymptotic Solutions of Linear Systems of Differential Equations with Two Small Parameters

Abstract

We consider a linear homogeneous system of differential equations with two small parameters. In this system, the dependence on one parameter is regular and on the other is singular. Using methods of the theory of perturbations of linear operators and a space analog of the Newton diagrams, we investigate the asymptotics of a general solution of this system in the case where its leading matrix has a multiple eigenvalue associated with a multiple elementary divisor.