The regularization method for singularly perturbed systems of nonlinear differential equations

The singularly perturbed Cauchy problem for systems of ordinary differential equations is studied. A regularized asymptotic solution for this problem is constructed by means of the method developed by S. A. Lomov for a broad class of linear systems and certain nonlinear scalar equations. In the course of constructing the asymptotic solution systems of partial differential equations containing a singularity are considered. For such systems a theory of normal and unique solvability in a class of uniformly convergent exponential series is developed. Asymptotic convergence of formal solutions is studied for the case of purely imaginary eigenvalues of the matrix of the first variation.
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