Geodesic
On contrast structures with a multizonal interior layer
Modelirovanie i analiz informacionnyh sistem, Tome 24 (2017) no. 3, pp. 288-308.

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A boundary value problem for a singularly perturbed differential equation of second order is considered in two cases, when one root of the degenerate equation is two-tuple. It is proved that in the first case the problem has a solution with the transition from the two-tuple root of the degenerate equation to one-tuple root in the small neighbourhood of an internal point of the interval, and in the second case the problem has a solution which has the spike in the interior layer. Such solutions are named, correspondingly, a contrast structure of step-type and a contrast structure of spike-type. In each case the asymptotic expansion of the contrast structure is constructed. It distinguishes from the known expansion in the case, when all the roots of the degenerate equation are one-tuple, in particular, the interior layer is multizonal.
Keywords: singularly perturbed equation, interior transitional layer, contrast structures of step type and spike type, asymptotic expansion of solution. 
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V. F. Butuzov. On contrast structures with a multizonal interior layer. Modelirovanie i analiz informacionnyh sistem, Tome 24 (2017) no. 3, pp. 288-308. http://geodesic.mathdoc.fr/item/MAIS_2017_24_3_a3/

[1] Vasilieva A. B., Butuzov V. F., Asymptotic methods in the theory of singular perturbations, Visshaya shkola, M., 1990 (in Russian) | MR

[2] Butuzov V. F., “Singularly perturbed boundary value problem with multizonal interior transitional layer”, Modeling and Analysis of Information Systems, 22:1 (2015), 5–22 (in Russian)

[3] Butuzov V. F., “On the special properties of the boundary layer in singularly perturbed problems with multiple root of the degenerate equation”, Mathematical Notes, 94:1 (2013), 60–70 | DOI | DOI | MR | Zbl