Construction of a General Solution of a Degenerate Linear System of Differential Equations with Irregular Singular Point

Abstract

We investigate the asymptotic behavior of the general solution of the linear system of differential equations with irregular singular point $$x^{ - h} B(x)\frac{{dy}}{{dt}} = A(x)y$$ in the case where the limit matrix of the coefficients of the derivatives is degenerate. We deduce a branching equation whose coefficients contain complete information on the structure of the general solution of the system considered in the case of multiple finite and infinite elementary divisors of the regular pencil of matrices L(λ) = A0 − λB0.