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 Mat. Zametki, 1998, Volume 63, Issue 3, Pages 354–362 (Mi mz1289)

A singularly perturbed boundary value problem for a second-order equation in the case of variation of stability

V. F. Butuzov, N. N. Nefedov

M. V. Lomonosov Moscow State University

Abstract: A boundary value problem for a second-order nonlinear singularly perturbed differential equation is considered for the case in which there is variation of stability caused by the intersection of roots of the degenerate equation. By the method of differential inequalities, we prove the existence of a solution such that the limit solution is nonsmooth.

DOI: https://doi.org/10.4213/mzm1289

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English version:
Mathematical Notes, 1998, 63:3, 311–318

Bibliographic databases:

UDC: 517.956.226

Citation: V. F. Butuzov, N. N. Nefedov, “A singularly perturbed boundary value problem for a second-order equation in the case of variation of stability”, Mat. Zametki, 63:3 (1998), 354–362; Math. Notes, 63:3 (1998), 311–318

Citation in format AMSBIB
\Bibitem{ButNef98} \by V.~F.~Butuzov, N.~N.~Nefedov \paper A singularly perturbed boundary value problem for a second-order equation in the case of variation of stability \jour Mat. Zametki \yr 1998 \vol 63 \issue 3 \pages 354--362 \mathnet{http://mi.mathnet.ru/mz1289} \crossref{https://doi.org/10.4213/mzm1289} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1631928} \zmath{https://zbmath.org/?q=an:0920.34023} \transl \jour Math. Notes \yr 1998 \vol 63 \issue 3 \pages 311--318 \crossref{https://doi.org/10.1007/BF02317775} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000075783100004} 

• http://mi.mathnet.ru/eng/mz1289
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• http://mi.mathnet.ru/eng/mz/v63/i3/p354

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Butuzov, VF, “Singularly perturbed boundary value problems for systems of Tichonov's type in case of exchange of stabilities”, Journal of Differential Equations, 159:2 (1999), 427
2. V. F. Butuzov, E. A. Gromova, “A limit theorem for a Tikhonov system of equations”, Comput. Math. Math. Phys., 40:5 (2000), 669–679
3. Butuzov, VF, “Singularly perturbed elliptic problems in the case of exchange of stabilities”, Journal of Differential Equations, 169:2 (2001), 373
4. V. F. Butuzov, E. A. Gromova, “Boundary value problem for a system of fast and slow second-order equations in the case of intersecting roots of the degenerate equation”, Comput. Math. Math. Phys., 41:8 (2001), 1108–1121
5. Butuzov, VF, “Singularly perturbed partly dissipative reaction-diffusion systems in case of exchange of stabilities”, Journal of Mathematical Analysis and Applications, 273:1 (2002), 217
6. Butuzov, VF, “Singularly perturbed parabolic equation in the case of intersecting roots of the degenerate equation”, Russian Journal of Mathematical Physics, 9:1 (2002), 50
7. V. F. Butuzov, N. N. Nefedov, K. R. Schneider, “On a singularly perturbed system of parabolic equations in the case of intersecting roots of the degenerate equation”, Comput. Math. Math. Phys., 42:2 (2002), 176–187
8. V. F. Butuzov, M. A. Terent'ev, “System of singularly perturbed equations in the case of intersecting roots of a degenerate system”, Comput. Math. Math. Phys., 42:11 (2002), 1622–1635
9. V. F. Butuzov, E. A. Gromova, “Singularly perturbed parabolic problem in the case of intersecting roots of the degenerate equation”, Proc. Steklov Inst. Math. (Suppl.), 2003no. , suppl. 1, S37–S44
10. N. N. Nefedov, K. R. Schneider, “Delay of exchange of stabilities in singularly perturbed parabolic problems”, Proc. Steklov Inst. Math. (Suppl.), 2003no. , suppl. 1, S144–S154
11. Comput. Math. Math. Phys., 44:7 (2004), 1213–1220
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13. Dolbeeva, SF, “Asymptotic behavior of the solution to a differential equation with a small parameter when the stability lines of the limit solution intersect”, Doklady Mathematics, 73:3 (2006), 388
14. V. F. Butuzov, “On the stability and domain of attraction of a stationary nonsmooth limit solution of a singularly perturbed parabolic equation”, Comput. Math. Math. Phys., 46:3 (2006), 413–424
15. S. F. Dolbeeva, E. A. Chizh, “Asymptotics of a second-order differential equation with a small parameter in the case when the reduced equation has two solutions”, Comput. Math. Math. Phys., 48:1 (2008), 30–42
16. Comput. Math. Math. Phys., 48:1 (2008), 43–58
17. Kadalbajoo M.K., Gupta V., “A Brief Survey on Numerical Methods for Solving Singularly Perturbed Problems”, Appl. Math. Comput., 217:8 (2010), 3641–3716
18. M. A. Terentev, “Ob otsutstvii i razrushenii reshenii v nekotorykh singulyarno vozmuschennykh zadachakh so smenoi ustoichivosti”, Model. i analiz inform. sistem, 23:5 (2016), 587–594
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