Systems of Linear Differential Equations of Rational Rank with Multiple Root of Characteristic Equation
نویسنده
چکیده
where ε = μq, ε p q = μp. The systems for which small parameter has a fractional power were studied by V.K. Grigorenko in [1]. The case of the simple roots of the characteristic equations and the case of the equation having only one multiple n root were studied separately. Let us construct the asymptotic solution of the system (1) by the method of perturbed characteristic equation [2] for the case when the matrix A0(t) is such that the characteristic equation has one multiple root λ0, to which m 1 multiple elementary divisors correspond. It means that there is non-degenerate matrix T (t) which leads matrix A0(t) to the matrix with the simplest structure of quasi-diagonal type
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