Geodesic
Solution of the singularly perturbed Cauchy problem with a ``weak'' turning point of the limit operator
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 3, Tome 192 (2021), pp. 55-64

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In this paper, we propose a method for constructing an asymptotic solution to a singularly perturbed Cauchy problem in the case of violation of the stability conditions for the spectrum of the limit operator. In particular, we consider a problem with a turning point where eigenvalues coincide at $t=0$.
Keywords: singularly perturbed problem, turning point, regularization method. 
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     author = {A. G. Eliseev and P. V. Kirichenko},
     title = {Solution of the singularly perturbed {Cauchy} problem with a ``weak'' turning point of the limit operator},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {55--64},
     publisher = {mathdoc},
     volume = {192},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_192_a5/}
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A. G. Eliseev; P. V. Kirichenko. Solution of the singularly perturbed Cauchy problem with a ``weak'' turning point of the limit operator. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 3, Tome 192 (2021), pp. 55-64. http://geodesic.mathdoc.fr/item/INTO_2021_192_a5/