Geodesic
On the Dependence of the Structure of Boundary Layers on the Boundary Conditions in a Singularly Perturbed Boundary-Value Problem with Multiple Root of the Related Degenerate Equation
Matematičeskie zametki, Tome 99 (2016) no. 2, pp. 201-214

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We consider the two-point boundary-value problem for a singularly perturbed second-order differential equation for the case in which the related degenerate equation has a double root. It is shown that the structure of boundary layers essentially depends on the degree of proximity of the given boundary values of the solution to the root of the degenerate equation; this phenomenon is determined by the multiplicity of the root.
Keywords: singularly perturbed second-order differential equation, boundary layer, two-point boundary-value problem, three-zone boundary layer, asymptotics of the boundary-layer solution. 
@article{MZM_2016_99_2_a4,
     author = {V. F. Butuzov},
     title = {On the {Dependence} of the {Structure} of {Boundary} {Layers} on the {Boundary} {Conditions} in a {Singularly} {Perturbed} {Boundary-Value} {Problem} with {Multiple} {Root} of the {Related} {Degenerate} {Equation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {201--214},
     publisher = {mathdoc},
     volume = {99},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_99_2_a4/}
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V. F. Butuzov. On the Dependence of the Structure of Boundary Layers on the Boundary Conditions in a Singularly Perturbed Boundary-Value Problem with Multiple Root of the Related Degenerate Equation. Matematičeskie zametki, Tome 99 (2016) no. 2, pp. 201-214. http://geodesic.mathdoc.fr/item/MZM_2016_99_2_a4/