Geodesic
A solution of the singularly perturbed Cauchy problem in the presence of a > turning point at the limit operator
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 51-60

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The paper proposes a method for constructing an asymptotic solution of the singularly perturbed Cauchy problem in the case of violation of the stability conditions of the spectrum of the limit operator. In particular, we consider the problem with a turning point where eigenvalues "stick together" at $t=0$.
Keywords: singularly perturbed Cauchy problem, turning point, regularization method. 
@article{SEMR_2020_17_a78,
     author = {A. G. Eliseev and P. V. Kirichenko},
     title = {A solution of the singularly perturbed {Cauchy} problem in the presence of a <<weak>> turning point at the limit operator},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {51--60},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a78/}
}
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A. G. Eliseev; P. V. Kirichenko. A solution of the singularly perturbed Cauchy problem in the presence of a <> turning point at the limit operator. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 51-60. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a78/