Geodesic
Stability of solutions to the Cauchy problem with respect to linear approximation, and branching equation in the root subspace
Informatics and Automation, Differential equations and dynamical systems, Tome 278 (2012), pp. 260-268.

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

V. A. Trenogin's results on the stability of solutions to the Cauchy problem for differential equations in Banach spaces with respect to linear approximation in the case of degenerate linearization are presented from the viewpoint of branching equation in the root subspace. 
@article{TRSPY_2012_278_a23,
     author = {V. A. Trenogin and B. V. Loginov and L. R. Kim-Tyan},
     title = {Stability of solutions to the {Cauchy} problem with respect to linear approximation, and branching equation in the root subspace},
     journal = {Informatics and Automation},
     pages = {260--268},
     publisher = {mathdoc},
     volume = {278},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2012_278_a23/}
}
TY  - JOUR
AU  - V. A. Trenogin
AU  - B. V. Loginov
AU  - L. R. Kim-Tyan
TI  - Stability of solutions to the Cauchy problem with respect to linear approximation, and branching equation in the root subspace
JO  - Informatics and Automation
PY  - 2012
SP  - 260
EP  - 268
VL  - 278
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2012_278_a23/
LA  - ru
ID  - TRSPY_2012_278_a23
ER  - 
%0 Journal Article
%A V. A. Trenogin
%A B. V. Loginov
%A L. R. Kim-Tyan
%T Stability of solutions to the Cauchy problem with respect to linear approximation, and branching equation in the root subspace
%J Informatics and Automation
%D 2012
%P 260-268
%V 278
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2012_278_a23/
%G ru
%F TRSPY_2012_278_a23
V. A. Trenogin; B. V. Loginov; L. R. Kim-Tyan. Stability of solutions to the Cauchy problem with respect to linear approximation, and branching equation in the root subspace. Informatics and Automation, Differential equations and dynamical systems, Tome 278 (2012), pp. 260-268. http://geodesic.mathdoc.fr/item/TRSPY_2012_278_a23/

[1] Trenogin V.A., “Teorema Lyapunova ob ustoichivosti po lineinomu priblizheniyu kak sledstvie teoremy o neyavnykh operatorakh”, DAN, 407:6 (2006), 742–746 | MR

[2] Trenogin V.A., “Two reduction schemes in investigation of stability by Lyapounov and asymptotic stability for abstract parabolic differential equations”, ROMAI Journal, 4:2 (2008), 169 | MR | Zbl

[3] Trenogin V.A., “Lineinoe priblizhenie dlya differentsialnykh uravnenii v banakhovom prostranstve i ustoichivost po Lyapunovu”, DAN, 428:4 (2009), 458–461 | MR | Zbl

[4] Trenogin V.A., “Ob ustoichivosti trivialnogo polozheniya ravnovesiya dlya DU s vyrozhdennoi lineinoi chastyu”, Matematicheskoe modelirovanie i differentsialnye uravneniya, Ch. 2 (Minsk, 2009), Tez. dokl. Mezhdunar. konf., Belorus. gos. un-t, Minsk, 2009, 170–171

[5] Vainberg M.M., Trenogin V.A., Teoriya vetvleniya reshenii nelineinykh uravnenii, Nauka, M., 1969 | MR

[6] Loginov B.V., Teoriya vetvleniya reshenii nelineinykh uravnenii v usloviyakh gruppovoi invariantnosti, Fan, Tashkent, 1985 | MR | Zbl

[7] Loginov B.V., Rusak Yu.B., “Generalized Jordan structure in the problem of the stability of bifurcating solutions”, Nonlinear Anal., Theory Methods Appl., 17:3 (1991), 219 | DOI | MR | Zbl

[8] Loginov B.V., Kim-Tyan L.R., Rusak Yu.B., “Modifikatsiya metoda Lyapunova–Shmidta i ustoichivost reshenii differentsialnykh uravnenii s vyrozhdennym operatorom konechnogo indeksa pri proizvodnoi”, DAN, 330:6 (1993), 687–690 | MR | Zbl

[9] Loginov B.V., Rusak Yu.B., “Obobschennaya zhordanova struktura v teorii vetvleniya”, Pryamye i obratnye zadachi dlya differentsialnykh uravnenii s chastnymi proizvodnymi i ikh prilozheniya, Fan, Tashkent, 1978, 133–148 | MR

[10] Trenogin V.A., Funktsionalnyi analiz, Nauka, M., 1980 | MR | Zbl

[11] Karasözen B., Konopleva I., Loginov B., “Hereditary symmetry of resolving systems for nonlinear equations with Fredholm operators”, Nonlinear analysis and applications, To V. Lakshmikantham on his 80th birthday, V. 2, Ed. by R.P. Agarwal, D. O'Regan, Kluwer, Dordrecht, 2003, 617–644 | MR | Zbl

[12] Loginov B.V., “Branching equation in the root subspace”, Nonlinear Anal., Theory Methods Appl., 32:3 (1998), 439–448 | DOI | MR | Zbl

[13] Demidovich B.P., Lektsii po matematicheskoi teorii ustoichivosti, Nauka, M., 1967 | MR

[14] Ovsyannikov L.V., “Programma podmodeli. Gazovaya dinamika”, PMM, 58:4 (1994), 30–55 | MR | Zbl

[15] Ovsyannikov L.V., Gruppovye svoistva differentsialnykh uravnenii, Izd-vo SO AN SSSR, Novosibirsk, 1962 | MR

[16] Ovsyannikov L.V., Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978 | MR | Zbl

[17] Sidorov N.A., Abdullin V.R., “Spletaemye uravneniya razvetvleniya v teorii nelineinykh uravnenii”, Mat. sb., 192:7 (2001), 107–124 | DOI | MR | Zbl

[18] Loginov B.V., Konopleva I.V., “Symmetry of resolving systems in degenerated functional equations”, Simmetriya i differentsialnye uravneniya, Tr. II Mezhdunar. konf. (Krasnoyarsk, 2000), In-t vychisl. modelirovaniya SO RAN, Krasnoyarsk, 2000, 145–148

[19] Loginov B.V., Konopleva I.V., “Symmetry of resolving system for differential equation with Fredholm operator at the derivative”, MOGRAN 2000: Modern group analysis for the new millenium, Proc. Int. Conf. (Ufa, 2000), Ufa State Aviation Tech. Unuv., Ufa, 2001, 116–119

[20] Kim-Tyan L.R., Loginov B.V., Rousak Yu.B., “Stability of bifurcating periodical solutions at Poincaré–Andronov–Hopf bifurcation for singular differential equations in Banach spaces”, ROMAI J., 6:1 (2010), 107–118 | MR | Zbl