The asymptotic solution of the bisingular Robin problem
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 10-21.

Voir la notice de l'article provenant de la source Math-Net.Ru

The modified method of boundary functions constructed full, uniform asymptotic expansion of the solution bisingular Robin problem for a second order ordinary differential equations with turning points in the real axis. Constructed uniform asymptotic expansion of the solution of the Robin problem justified by the principle of maximum.
Keywords: asymptotic expansion, bisingularly problem, Robin problem, small parameter, boundary function.
@article{SEMR_2017_14_a82,
     author = {D. A. Tursunov},
     title = {The asymptotic solution of the bisingular {Robin} problem},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {10--21},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a82/}
}
TY  - JOUR
AU  - D. A. Tursunov
TI  - The asymptotic solution of the bisingular Robin problem
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2017
SP  - 10
EP  - 21
VL  - 14
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2017_14_a82/
LA  - ru
ID  - SEMR_2017_14_a82
ER  - 
%0 Journal Article
%A D. A. Tursunov
%T The asymptotic solution of the bisingular Robin problem
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2017
%P 10-21
%V 14
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2017_14_a82/
%G ru
%F SEMR_2017_14_a82
D. A. Tursunov. The asymptotic solution of the bisingular Robin problem. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 10-21. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a82/

[1] W. Wasow, Asymptotic Expansions for Ordinary Differential Equations, Dover publications, INC, Mineola–New York, 1965 | MR

[2] W. Wasow, Linear turning point theory, Springer-Verlag, New York, 1985 | MR | Zbl

[3] F. M. Olver, “Connection formulas for second-order differential equations with multiple turning points”, SIAM. J. Math. Anal., 1:8 (1977), 127–154 | DOI | MR

[4] F. M. Olver, “Connection formulas for second-order differential equations having an arbitrary number of turning points of arbitrary multiplicities”, SIAM. J. Math. Anal., 4:8 (1977), 673–700 | DOI | MR

[5] A. M. Il'in, Matching of asymptotic expansions of solutions of boundary value problems, Amer. Math. Soc., Providence, RI, 1992 | MR | Zbl

[6] A. M. Il'in, A. R. Danilin, Asymptotic Methods in Analysis, Fizmatlit, M., 2009 (in Russian) | Zbl

[7] V. N. Bobochko, “Uniform Asymptotics of a Solution of an Inhomogeneous System of Two Differential Equations with a Turning Point”, Russian Mathematics, 50:5 (2006), 6–16 | MR | Zbl

[8] V. N. Bobochko, “An Unstable Differential Turning Point in the Theory of Singular Perturbations”, Russian Mathematics, 49:4 (2005), 6–14 | MR | Zbl

[9] 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”, Math. Notes, 94:4 (2013), 451–454 | DOI | MR | Zbl

[10] K. Alymkulov, D. A. Tursunov, “On a method of construction of asymptotic decompositions of bisingular perturbed problems”, Russian Mathematics, 60:12 (2016), 1–8 | DOI

[11] D. A. Tursunov, “Asymptotic expansion for a solution of an ordinary second-order differential equation with three turning points”, Tr. IMM UrO RAN, 22, no. 1, 2016, 271–281 | MR

[12] D. A. Tursunov, “Asymptotic expansion of the solution of a singularly perturbed ordinary second-order differential equation with two turning points”, Tomsk state university journal of mathematics and mechanics, 21:1 (2013), 34–40

[13] T. G. T. Carleman, Les fonctions quasi-analytiques, specially Chap. V, Paris, 1926

[14] A. Erdelyi, Asymptotic expansions, Dover publications, INC, New York, 1956 | MR | Zbl