On Nonoscillating Solutions of Emden--Fowler-Type Equations
Matematičeskie zametki, Tome 95 (2014) no. 6, pp. 911-925.

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

The asymptotic properties of nonoscillating solutions of Emden–Fowler-type equations of arbitrary order are considered. The paper contains the results of the study of the asymptotic properties of solutions with integer-valued asymptotics as well as of solutions arising from the rapid decrease of the coefficient of the equation. To analyze the asymptotic behavior of solutions of the equations, methods of power geometry are used.
Keywords: Emden–Fowler-type equation, power geometry, nonoscillating solution, noncontinuable solution, Newton polyhedron.
@article{MZM_2014_95_6_a11,
     author = {V. S. Samovol},
     title = {On {Nonoscillating} {Solutions} of {Emden--Fowler-Type} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {911--925},
     publisher = {mathdoc},
     volume = {95},
     number = {6},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_95_6_a11/}
}
TY  - JOUR
AU  - V. S. Samovol
TI  - On Nonoscillating Solutions of Emden--Fowler-Type Equations
JO  - Matematičeskie zametki
PY  - 2014
SP  - 911
EP  - 925
VL  - 95
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2014_95_6_a11/
LA  - ru
ID  - MZM_2014_95_6_a11
ER  - 
%0 Journal Article
%A V. S. Samovol
%T On Nonoscillating Solutions of Emden--Fowler-Type Equations
%J Matematičeskie zametki
%D 2014
%P 911-925
%V 95
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2014_95_6_a11/
%G ru
%F MZM_2014_95_6_a11
V. S. Samovol. On Nonoscillating Solutions of Emden--Fowler-Type Equations. Matematičeskie zametki, Tome 95 (2014) no. 6, pp. 911-925. http://geodesic.mathdoc.fr/item/MZM_2014_95_6_a11/

[1] V. S. Samovol, “O resheniyakh uravnenii tipa Emdena–Faulera”, Matem. zametki, 95:5 (2014), 775–789

[2] R. Bellman, Teoriya ustoichivosti reshenii differentsialnykh uravnenii, IL, M., 1954

[3] V. A. Kondratev, V. S. Samovol, “O nekotorykh asimptoticheskikh svoistvakh reshenii uravnenii tipa Emdena–Faulera”, Differents. uravneniya, 17:4 (1981), 749–750

[4] I. M. Sobol, “Ob asimptoticheskom povedenii reshenii lineinykh differentsialnykh uravnenii”, Dokl. AN SSSR, 61:2 (1948), 219–222 | MR | Zbl

[5] I. T. Kiguradze, “O koleblemosti reshenii uravneniya $\frac{d^mu}{dt^m}+a(t)|u|^n\operatorname{sign}u=0$”, Matem. sb., 65:2 (1964), 172–187 | MR | Zbl

[6] I. T. Kiguradze, T. F. Chanturiya, Asimptoticheskie svoistva reshenii neavtonomnykh obyknovennykh differentsialnykh uravnenii, Nauka, M., 1990

[7] N. A. Izobov, “O prodolzhimykh i neprodolzhimykh resheniyakh nelineinogo differentsialnogo uravneniya proizvolnogo poryadka”, Matem. zametki, 35:6 (1984), 829–839 | MR | Zbl

[8] I. V. Astashova, Kachestvennye svoistva reshenii differentsialnykh uravnenii i smezhnye voprosy spektralnogo analiza, YuNITI-DANA, M., 2012

[9] A. D. Bryuno, Stepennaya geometriya v algebraicheskikh i differentsialnykh uravneniyakh, Nauka, M., 1998 | MR

[10] A. D. Bryuno, “Asimptotiki i razlozheniya reshenii obyknovennogo differentsialnogo uravneniya”, UMN, 59:3 (2004), 31–80 | DOI | MR | Zbl