A system of singularly perturbed equations with differential turning point of the 1st kind
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2015), pp. 63-74.

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

For a system of differential equations with small parameter at the higher derivative and turning point we construct uniform asymptotics of the solution. We consider the case when the spectrum of the boundary operator contains multiple elements and elements that identically equal zero.
Keywords: linear system, small parameter, turning point, Airy operator.
@article{IVM_2015_3_a5,
     author = {I. A. Zelenskaya},
     title = {A system of singularly perturbed equations with differential turning point of the 1st kind},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {63--74},
     publisher = {mathdoc},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_3_a5/}
}
TY  - JOUR
AU  - I. A. Zelenskaya
TI  - A system of singularly perturbed equations with differential turning point of the 1st kind
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2015
SP  - 63
EP  - 74
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2015_3_a5/
LA  - ru
ID  - IVM_2015_3_a5
ER  - 
%0 Journal Article
%A I. A. Zelenskaya
%T A system of singularly perturbed equations with differential turning point of the 1st kind
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2015
%P 63-74
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2015_3_a5/
%G ru
%F IVM_2015_3_a5
I. A. Zelenskaya. A system of singularly perturbed equations with differential turning point of the 1st kind. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2015), pp. 63-74. http://geodesic.mathdoc.fr/item/IVM_2015_3_a5/

[1] Wasow W., Linear turning point theory, Springer-Verlag, N.Y., 1985 | MR | Zbl

[2] Bobochko V. M., Perestyuk M. O., Asimptotichne integruvannya rivnyannya Liuvillya z tochkami zvorotu, Nauk. dumka, Kiiv, 2002 | Zbl

[3] Lin C. C., Rabenstein A. L., “On the asymptotic theory of a class of ordinary differential equations of fourth order. II. Existense of solutions which are approximated by the formal solutions”, Stud. Appl. Math., 48:4 (1969), 311–340 | MR | Zbl

[4] Nakano M., Nishimoto T., “On an asymptotic expansion of solutions of ORR-Sommerfeld type equation”, Lect. Notes Math., 243, 1971, 315–319 | DOI | MR | Zbl

[5] Nishimoto T., “A turning point problem of an $n$-th order differential equation of hydrodynamic type”, Kōdai Math. Semin. Rep., 20:3 (1968), 218–256 | DOI | MR | Zbl

[6] Langer R. E., “On the asymptotic forms of ordinary differential equations of the third order in a region containing a turning point”, Trans. Amer. Math. Soc., 80:1 (1955), 93–123 | DOI | MR | Zbl

[7] Langer R. E., “The solutions of a class of linear ordinary differential equations of the third order in a region containing a multiple turning point”, Duke. Math. J., 23:1 (1956), 93–110 | DOI | MR | Zbl

[8] Bragg R. E., “Fundamental solutions of linear ordinary differential equation of the third order in the neighborhood of single second order turning point”, Duke. Math. J., 25:2 (1958), 239–254 | DOI | MR

[9] Bobochko V. N., “Differentsialnaya tochka povorota v teorii singulyarnykh vozmuschenii. I”, Izv. vuzov. Matem., 2002, no. 3, 3–14 | MR | Zbl

[10] Bobochko V. N., “Differentsialnaya tochka povorota v teorii singulyarnykh vozmuschenii. II”, Izv. vuzov. Matem., 2002, no. 5, 3–13 | MR | Zbl

[11] Hsieh P. F., “A turning point problem for a system of linear ordinary differential equations of the third order”, Arch. Rational Mech. Anal., 19:2 (1965), 117–148 | DOI | MR | Zbl

[12] Dorodnitsyn A. A., “Asimptoticheskie zakony raspredeleniya sobstvennykh znachenii dlya nekotorykh osobykh vidov differentsialnykh uravnenii vtorogo poryadka”, UMN, 7:6 (1952), 3–96 | MR | Zbl