On the Construction of a Solution of a Degenerate Linear System of Differential Equations in the Neighborhood of an Irregular Singular Point

Abstract

We investigate the asymptotics of the general solution of the linear system of differential equations with irregular singular point $$x^{ - h} B(x)\frac{{dy}}{{dx}} = A(x)y$$ in the case where the limit matrix coefficient of the derivative degenerates. Using the Newton diagram method, we construct the general solution of the system in the case where the regular pencil of matrices L(λ) = A0 − λB0 has multiple finite and infinite elementary divisors.