Geodesic
Application of resurgent analysis to the construction of asymptotics of linear differential equations with degeneration in coefficients
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17, St. Petersburg Polytechnic University, July 24-28, 2017, Tome 160 (2019), pp. 61-73.

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

This paper is a review of results concerning the construction of asymptotics of solutions to degenerate linear differential equations with holomorphic coefficients. We consider both cases of ordinary and partial differential equations.
Keywords: irregular singular points, resurgent analysis, asymptotics. 
@article{INTO_2019_160_a7,
     author = {M. V. Korovina},
     title = {Application of resurgent analysis to the construction of asymptotics of linear differential equations with degeneration in coefficients},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {61--73},
     publisher = {mathdoc},
     volume = {160},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_160_a7/}
}
TY  - JOUR
AU  - M. V. Korovina
TI  - Application of resurgent analysis to the construction of asymptotics of linear differential equations with degeneration in coefficients
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2019
SP  - 61
EP  - 73
VL  - 160
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2019_160_a7/
LA  - ru
ID  - INTO_2019_160_a7
ER  - 
%0 Journal Article
%A M. V. Korovina
%T Application of resurgent analysis to the construction of asymptotics of linear differential equations with degeneration in coefficients
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2019
%P 61-73
%V 160
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2019_160_a7/
%G ru
%F INTO_2019_160_a7
M. V. Korovina. Application of resurgent analysis to the construction of asymptotics of linear differential equations with degeneration in coefficients. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17, St. Petersburg Polytechnic University, July 24-28, 2017, Tome 160 (2019), pp. 61-73. http://geodesic.mathdoc.fr/item/INTO_2019_160_a7/

[1] Volnukhin M. S., “Asimptotiki reshenii differentsialnykh uravnenii s vyrozhdeniyami v sluchae rezonansa”, Dokl. RAN, 449:3 (2013), 259–262 | DOI | MR | Zbl

[2] Volnukhin M. S., “Rezonansnyi sluchai dlya differentsialnykh uravnenii s vyrozhdeniem”, Differ. uravn., 50:3 (2014), 339–348 | DOI | MR | Zbl

[3] Kats D. S., “Vychislenie asimptotik reshenii uravnenii s polinomialnymi vyrozhdeniyami koeffitsientov”, Differ. uravn., 51:12 (2015), 1612–1617 | DOI | Zbl

[4] Kats D. S., “Koeffitsienty ryadov v asimptoticheskikh razlozheniyakh reshenii uravnenii s vyrozhdeniyami”, Int. J. Open Inform. Techn., 4:9 (2016), 1–7

[5] Koddington E. A., Levinson N., Teoriya obyknovennykh differentsialnykh uravnenii, IL, M., 1958

[6] Kondratev V. A., “Kraevye zadachi dlya ellipticheskikh uravnenii v oblastyakh s konicheskimi ili uglovymi tochkami”, Tr. Mosk. mat. o-va, 16, 1967, 209–292 | Zbl

[7] Kondratev V. A., “Kraevye zadachi dlya ellipticheskikh uravnenii v konicheskikh oblastyakh”, Dokl. AN SSSR, 153:1 (1963), 27–29 | Zbl

[8] Korovina M. V., “Suschestvovanie resurgentnogo resheniya dlya uravnenii s vyrozhdeniem vysshikh poryadkov”, Differ. uravn., 47:3 (2011), 349–357 | MR

[9] Korovina M. V., “Asimptotiki reshenii uravnenii s vysshimi vyrozhdeniyami”, Dokl. RAN, 437:3 (2011), 302–304 | Zbl

[10] Korovina M. V., “Asimptotiki reshenii uravnenii vtorogo poryadka so starshimi vyrozhdeniyami i uravnenie Laplasa na mnogoobrazii s osobennostyu tipa klyuva”, Dokl. RAN, 456:4 (2014), 396–399 | DOI | Zbl

[11] Korovina M. V., “Metod povtornogo kvantovaniya i ego primeneniya k postroeniyu asimptotik reshenii uravnenii s vyrozhdeniyami”, Differ. uravn., 52:1 (2016), 60–77 | DOI | Zbl

[12] Korovina M. V., Shatalov V. E., “Differentsialnye uravneniya s vyrozhdeniem i resurgentnyi analiz”, Differ. uravn., 46:9 (2010), 1259–1277 | MR | Zbl

[13] Korovina M. V., Shatalov V. E., “Differentsialnye uravneniya s vyrozhdeniem”, Dokl. RAN, 437:1 (2011), 16–19 | Zbl

[14] Olver F., Asimptotika i spetsialnye funktsii, Nauka, M., 1990

[15] Sternin B. Yu., Shatalov V. E., “Differentsialnye uravneniya v prostranstvakh s asimptotikami na mnogoobraziyakh s osobennostyami tipa klyuva”, Differ. uravn., 38:12 (2002), 1664—1672 | MR | Zbl

[16] Chezari L., Asimptoticheskoe povedenie i ustoichivost reshenii obyknovennykh differentsialnykh uravnenii, Mir, M., 1964

[17] Ecalle J., Cinq applications des fonctions résurgentes, Pub. Math. d'Orsay, 1984

[18] Korovina M. V., “Asymptotic solutions of second-order equations with holomorphic coefficients with degeneracies and Laplace's equations on a manifold with a cuspidal singularity”, Global J. Sci. Front. Res. F.: Math. Decision Sci., 17:6 (2017), 57–71

[19] Schulze B.-W., Sternin B., Shatalov V., Asymptotic solutions to differential equations on manifolds with cusps, Preprint MPI 96-89, Max-Planck-Institut für Mathematik, Bonn, 1996 | MR

[20] Schulze B.-W., Sternin B., Shatalov V., “An operator algebra on manifolds with cusp-type singularities”, Ann. Global Anal. Geom., 16:2 (1998), 101–140 | DOI | MR | Zbl

[21] Sternin B., Shatalov V., Borel–Laplace Transform and Asymptotic Theory. Introduction to Resurgent Analysis, CRC Press, 1996 | MR | Zbl