Asymptotics of the General Solution of Linear Singularly Perturbed Systems of Higher-Order Differential Equations with Degeneration in the Case of Multiple Spectrum of the Limiting Matrix Pencil

Abstract

We construct an asymptotic expansion for the fundamental system of solutions of a linear singularly perturbed system of m-order differential equations with degenerate principal matrix at the higher-order derivatives. The case where the corresponding characteristic polynomial has a multiple spectrum is investigated. It is proved that, in this case, the asymptotic expansions are constructed in the fractional powers of the small parameter. The recurrence formulas for the coefficients of these expansions are obtained.