Pafyc S. Construction of the asymptotic solution of linear singularly perturbed systems of higher order differential equations with degenerations

The dissertation research is devoted to the construction of asymptotic of the general solution of linear singularly perturbed system of higher order differential equations in which the matrix of the highest derivative is degenerate. The limit polynomial bundle of matrixes is regular and has stable Kronecker structure at a predetermined interval. It was found that under these conditions, the system of equations has the general solution of the Cauchy type, determined its structure and developed an algorithm for constructing asymptotic expansions the small parameter to zero the basal linearly independent solutions of the homogeneous system and part of the solution of the inhomogeneous in different cases related to the Kronecker structure limit beam matrix. In the case where the beam has a limit of one times the final and everlasting elementary divisors, carried out a full analysis of the general asymptotic solution of the corresponding homogeneous system using the method of Newton diagrams. The results which have established earlier by other authors for systems of the first and second order equations are following from obtained results.