Generalization of the Boundary Function Method for Solving Boundary-Value Problems for Bisingularly Perturbed Second-Order Differential Equations
Matematičeskie zametki, Tome 94 (2013) no. 4, pp. 483-487.

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A bisingular boundary-value problem for an ordinary differential equation is considered. The asymptotics of the solution as the sum of an outer expansion and an analog of a number of functions of the boundary layer is constructed.
Keywords: bisingularly perturbed differential equation, boundary-value problem, boundary function method, maximum principle.
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K. Alymkulov; T. D. Asylbekov; S. F. Dolbeeva. Generalization of the Boundary Function Method for Solving Boundary-Value Problems for Bisingularly Perturbed Second-Order Differential Equations. Matematičeskie zametki, Tome 94 (2013) no. 4, pp. 483-487. http://geodesic.mathdoc.fr/item/MZM_2013_94_4_a0/

[1] A. M. Ilin, Soglasovanie asimptoticheskikh razlozhenii reshenii kraevykh zadach, Nauka, M., 1989 | MR | Zbl

[2] E. M. de Jager, F. Jiang, The Theory of Singular Perturbations, North-Holland Ser. Appl. Math. Mech., 42, North-Holland Publ., Amsterdam, 1996 | MR

[3] J. Hadamard, Le problème de Cauchy et les équations aux dérivées partielles linéares hyperboliques, Hermann, Paris, 1932 | Zbl

[4] A. B. Vasileva, V. F. Butuzov, Asimptoticheskie metody v teorii singulyarnykh vozmuschenii, Aktualnye voprosy prikladnoi i vychislitelnoi matematiki, Vysshaya shkola, M., 1990 | MR | Zbl

[5] M. H. Protter, H. F. Weinberger, Maximum Principles in Differential Equations, Englewood Cliffs, NJ, Prentice-Hall, 1967 | MR | Zbl

[6] A. M. Ilin, A. R. Danilin, Asimptoticheskie metody v analize, Fizmatlit, M., 2009 | Zbl

[7] K. V. Emelyanov, “Ob asimptotike resheniya pervoi kraevoi zadachi dlya uravneniya $\varepsilon u''(x)+xa(x)u'(x)-b(x)u=f(x)$”, Primenenie metoda soglasovaniya asimptoticheskikh razlozhenii k kraevym zadacham dlya differentsialnykh uravnenii, Tr. In-ta matem. i mekh. UNTs AN SSSR, 28, Sverdlovsk, 1979, 5–14 | MR | Zbl

[8] K. Alymkulov, A. Z. Zulpukarov, “Ravnomernoe priblizhenie resheniya kraevoi zadachi singulyarno vozmuschennogo uravneniya vtorogo poryadka v sluchae, kogda nevozmuschennoe uravnenie imeet regulyarnuyu osobuyu tochku”, Issledovaniya po integro-differentsialnym uravneniyam, 33, AN KirgSSR, In-t matem., Bishkek, 1990, 118–122