Geodesic
Implicit operator theorems under group symmetry conditions
The Bulletin of Irkutsk State University. Series Mathematics, Tome 4 (2011) no. 1, pp. 31-43

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On the base of the general theorem about the inheritance of nonlinear problem group symmetry by the relevant branching equation and branching equation in the root-subspace $G$-invariant implicit operator theorems are proved for stationary and nonstationary bifurcation problems without assumtion on compactness of allowing group.
Keywords: Lyapounov–Schmidt method, branching equation, branching equation in the root-subspaces, group symmetry. 
B. V. Loginov; I. V. Konopleva; Y. B. Rousak. Implicit operator theorems under group symmetry conditions. The Bulletin of Irkutsk State University. Series Mathematics, Tome 4 (2011) no. 1, pp. 31-43. http://geodesic.mathdoc.fr/item/IIGUM_2011_4_1_a3/
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[1] I. V. Konopleva, B. V. Loginov, Yu. B. Rusak, “Simmetriya i potentsialnost uravnenii razvetvleniya v kornevykh podprostranstvakh v neyavno zadannykh statsionarnykh i dinamicheskikh bifurkatsionnykh zadachakh”, Izv. vysshikh ucheb. zavedenii. Sev.-Kavkaz. region. Estestvennye nauki, 2009, Spetsvypusk, 115–124

[2] I. V. Konopleva, B. V. Loginov, Yu. B. Rusak, “Simmetriya i potentsialnost uravnenii razvetvleniya v kornevykh podprostranstvakh v neyavno zadannykh statsionarnykh bifurkatsionnykh zadachakh”, Analiticheskie metody analiza i differentsialnykh uravnenii AMADE, Tr. 5-i mezhdunar. konf. (Belarus, Minsk, 14–19 sentyabrya 2009 g.), v. 1, 2009, 90–95 | MR

[3] Doklady Mathematics, 80:1 (2009), 541–546 | DOI | MR | Zbl

[4] B. V. Loginov, I. V. Konopleva, Yu. B. Rusak, “Simmetriya i potentsialnost v obschei zadache teorii vetvleniya”, Izv. vuzov. Matematika, 2006, no. 4(527), 30–40 | MR | Zbl

[5] B. V. Loginov, “Obschaya zadacha teorii vetvleniya v usloviyakh gruppovoi simmetrii”, Uzbek. mat. zhurn., 1991, no. 1, 38–44

[6] N. I. Makarenko, “O vetvlenii reshenii invariantnykh variatsionnykh uravnenii”, DAN. Matematika, 348:3 (1996), 302–304 | MR | Zbl

[7] N. I. Makarenko, “Simmetriya i kosimmetriya variatsionnykh zadach v teorii voln”, Primenenie simmetrii i kosimmetrii v teorii bifurkatsii i fazovykh perekhodov, Tr. mezhdunar. shkoly-seminara (Sochi, 14–18 sentyabrya 2001 g.), Rostov. gos. un-t, Rostov n/D., 2001, 109–120

[8] B. V. Loginov, O. V. Makeev, I. V. Konopleva, Yu. B. Rousak, “Bifurcation and symmetry in differential equations non-resolved with respect to derivative”, ROMAI J., 3:1 (2007), 151–173 | MR | Zbl