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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2005, Volume 45, Number 3, Pages 472–483 (Mi zvmmf688)  
Steplike contrast structures for a second-order singularly perturbed quasilinear differential equation in the critical case

O. E. Omel'chenko

Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkovskaya ul. 3, Kiev, 01601, Ukraine
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Abstract: For a second-order singularly perturbed differential equation that is linear with respect to the derivative, a solution is considered that has an interior steplike transition layer in the critical case. An asymptotic expansion of the solution with respect to a small parameter is constructed and substantiated. An equation for the transition point is derived.
Key words: contrast structures, singularly perturbed ODE, critical case, asymptotic expansion.
Received: 25.05.2004
Bibliographic databases:
Document Type: Article
UDC: 519.624.2
Language: Russian
Citation: O. E. Omel'chenko, “Steplike contrast structures for a second-order singularly perturbed quasilinear differential equation in the critical case”, Zh. Vychisl. Mat. Mat. Fiz., 45:3 (2005), 472–483; Comput. Math. Math. Phys., 45:3 (2005), 454–464
Citation in format AMSBIB
\Bibitem{Ome05}
\by O.~E.~Omel'chenko
\paper Steplike contrast structures for a second-order singularly perturbed quasilinear differential equation in the critical case
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2005
\vol 45
\issue 3
\pages 472--483
\mathnet{http://mi.mathnet.ru/zvmmf688}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2161488}
\zmath{https://zbmath.org/?q=an:1079.34529}
\transl
\jour Comput. Math. Math. Phys.
\yr 2005
\vol 45
\issue 3
\pages 454--464
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