Geodesic
The regularization method for singularly perturbed systems of nonlinear differential equations
Izvestiya. Mathematics , Tome 14 (1980) no. 3, pp. 571-596

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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. Bibliography: 16 titles. 
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     author = {V. F. Safonov},
     title = {The regularization method for singularly perturbed systems of nonlinear differential equations},
     journal = {Izvestiya. Mathematics },
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     volume = {14},
     number = {3},
     year = {1980},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1980_14_3_a3/}
}
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V. F. Safonov. The regularization method for singularly perturbed systems of nonlinear differential equations. Izvestiya. Mathematics , Tome 14 (1980) no. 3, pp. 571-596. http://geodesic.mathdoc.fr/item/IM2_1980_14_3_a3/