Asymptotic expansions of the solutions of linear,singularly perturbed differential equations

Asymptotic expansions are constructed for the general solution of a finitedimensional singularly perturbed linear differential equation in cases of strong degeneracy of the structure matrix. For additional restrictions on the elements of the structure matrix these cases can be reduced to the case when the new structure matrix is nondegenerate.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Institute im. V. A. Steklova AN SSSR, Vol. 195, pp. 161–178, 1991.The author deeply thanks S. G. Krein, A. P. Oskolov, and V. M. Babich for useful discussions.