Geodesic
The use of group properties to determine milti-parameter families of solutions of nonlinear equations
Sbornik. Mathematics, Tome 14 (1971) no. 3, pp. 438-452
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider a nonlinear equation in a Banach space which is invariant relative to a continuous group. We give conditions which allow us to reduce Lyapunov–Schmidt branch equations in both the number of equations and the number of unknowns, which makes it possible to simplify significantly the search for multi-parameter families of solutions of the given problem. Bibliography: 15 titles. 
@article{SM_1971_14_3_a8,
     author = {B. V. Loginov and V. A. Trenogin},
     title = {The use of group properties to determine milti-parameter families of solutions of nonlinear equations},
     journal = {Sbornik. Mathematics},
     pages = {438--452},
     year = {1971},
     volume = {14},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1971_14_3_a8/}
}
TY  - JOUR
AU  - B. V. Loginov
AU  - V. A. Trenogin
TI  - The use of group properties to determine milti-parameter families of solutions of nonlinear equations
JO  - Sbornik. Mathematics
PY  - 1971
SP  - 438
EP  - 452
VL  - 14
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_1971_14_3_a8/
LA  - en
ID  - SM_1971_14_3_a8
ER  - 
%0 Journal Article
%A B. V. Loginov
%A V. A. Trenogin
%T The use of group properties to determine milti-parameter families of solutions of nonlinear equations
%J Sbornik. Mathematics
%D 1971
%P 438-452
%V 14
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1971_14_3_a8/
%G en
%F SM_1971_14_3_a8
B. V. Loginov; V. A. Trenogin. The use of group properties to determine milti-parameter families of solutions of nonlinear equations. Sbornik. Mathematics, Tome 14 (1971) no. 3, pp. 438-452. http://geodesic.mathdoc.fr/item/SM_1971_14_3_a8/

[1] A. M. Ter-Krikorov, V. A. Trenogin, “Suschestvovanie i asimptotika reshenii tipa “uedinennoi volny” dlya odnogo klassa nelineinykh ellipticheskikh uravnenii”, Matem. sb., 62(104) (1963), 264–274 | MR | Zbl

[2] A. M. Ter-Krikorov, V. A. Trenogin, “Resheniya tipa dlinnykh voln dlya kvazilineinykh ellipticheskikh uravnenii v neogranichennoi polose”, Diff. uravneniya, 3:3 (1967), 496–508 | MR | Zbl

[3] V. A. Trenogin, “Suschestvovanie i asimptotika reshenii tipa “uedinennoi volny” dlya differentsialnykh uravnenii v banakhovom prostranstve”, DAN SSSR, 156:5 (1964), 11033–1036 | MR

[4] W. Velte, “Stabilität und Verzweigung stationärer Lösungen der Navier–Stockesschen Gleidiungen beim Taylorproblem”, Arch. Rat. Mech. and Anal., 22:1 (1966), 1–14 | DOI | MR | Zbl

[5] V. I. Yudovich, “Vtorichnye techeniya i neustoichivost zhidkosti mezhdu vraschayuschimisya tsilindrami”, Prikl. matem. mekh., 30:4 (1966), 688–693

[6] Yu. P. Ivanilov, G. I. Yakovlev, “O bifurkatsii techenii zhidkosti mezhdu vraschayuschimisya tsilindrami”, Prikl. matem. mekh., 30:4 (1966), 768–773 | MR | Zbl

[7] S. N. Ovchinnikova, V. I. Yudovich, “Raschet vtorichnogo statsionarnogo techeniya mezhdu vraschayuschimisya tsilindrami”, Prikl. matem. mekh., 32:5 (1968), 858–868 | Zbl

[8] W. Velle, “Sur Stabilität der Strömung in einem horizontalen Rohr bei ungleichmässig erwärmter Wand”, ZAMP, 13 (1962), 591–600 | DOI

[9] M. P. Ukhovskii, V. I. Yudovich, “Ob uravneniyakh statsionarnoi konvektsii”, Prikl. matem. mekh., 27:2 (1963), 295–300 | MR

[10] W. Velle, “Stabilitatsverhalten und Verzweigung stationarer Losungen der Navier-Stokesschen Gleichungen”, Arch. Rat. Mech. and Anal., 16:2 (1964), 97–125 | DOI | MR

[11] V. I. Yudovich, “O vozniknovenii konvektsii”, Prikl. matem. mekh., 30:6 (1966), 1000–1005

[12] V. I. Yudovich, “Svobodnaya konvektsiya v vetvlenie”, Prikl. matem. mekh., 31:1 (1967), 101–111 | Zbl

[13] P. D. Lax, “Integrals of nonlinear equations of evolution and solitary waves”, Comm. Pure and Appl. Math., 21 (1968), 467–490 ; Matematika, 13:5 (1969), 128–150 | DOI | MR | Zbl

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

[15] L. P. Eizenkhart, Nepreryvnye gruppy preobrazovanii, IL, Moskva, 1947