Geodesic
A existance and a stability of solutions for semilinear Sobolev type equations in relatively radial case
The Bulletin of Irkutsk State University. Series Mathematics, Tome 6 (2013) no. 1, pp. 78-88 Cet article a éte moissonné depuis la source Math-Net.Ru

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The unique solvability of the Cauchy problem for a semilinear Sobolev type equation with respect to $p$-radial operators studied in this paper. Stability of the solutions in the neighborhood of zero has been studied for these equations.
Keywords: semilinear Sobolev type equations, theorem of Hadamar–Perron, stable and unstable manifold of solutions. 
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M. A. Sagadeeva. A existance and a stability of solutions for semilinear Sobolev type equations in relatively radial case. The Bulletin of Irkutsk State University. Series Mathematics, Tome 6 (2013) no. 1, pp. 78-88. http://geodesic.mathdoc.fr/item/IIGUM_2013_6_1_a7/

[1] V. I. Arnold, Yu. S. Ilyashenko, “Obyknovennye differentsialnye uravneniya”, Itogi nauki i tekhniki. Sovrem. problemy matematiki. Fundament. napravlenie, 1, 1985, 7–149 | MR

[2] S. A. Zagrebina, M. M. Yakupov, “Suschestvovanie i ustoichivost reshenii odnogo klassa polulineinykh uravnenii sobolevskogo tipa”, Vestn. YuUrGU. Ser. Mat. modelirovanie i programmirovanie, 2008, no. 2, 10–18 | Zbl

[3] O. G. Kitaeva, G. A. Sviridyuk, “Ustoichivoe i neustoichivoe invariantnye mnogoobraziya uravneniya Oskolkova”, Neklas. uravneniya mat. fiziki, Tr. seminara, posvyasch. 60-letiyu prof. V. N. Vragova, In-t matematiki im. S. L. Soboleva SO RAN, Novosibirsk, 2005, 161–166

[4] A. V. Keller, “Otnositelno spektralnaya teorema”, Vestn. Chelyab. gos. un-ta. Ser. Mat. mekhanika, 1996, no. 1(3), 62–66

[5] M. A. Sagadeeva, Dikhotomii reshenii lineinykh uravnenii sobolevskogo tipa, monografiya, Izd. tsentr YuUrGU, Chelyabinsk, 2012, 139 pp. | Zbl

[6] G. A. Sviridyuk, “Kvazistatsionarnye traektorii polulineinykh dinamicheskikh uravnenii tipa Soboleva”, Izv. RAN. Ser. mat., 57:3 (1993), 192–207 | MR | Zbl

[7] G. A. Sviridyuk, “Fazovye prostranstva polulineinykh uravnenii tipa Soboleva s otnositelno silno sektorialnym operatorom”, Algebra i analiz, 6:5 (1994), 252–272 | MR

[8] D. Khenri, Geometricheskaya teoriya polulineinykh parabolicheskikh uravnenii, Per. s angl., Mir, M., 1985, 376 pp. | MR

[9] V. E. Fedorov, M. A. Sagadeeva, “Suschestvovanie eksponentsialnykh dikhotomii nekotorykh klassov vyrozhdennykh lineinykh uravnenii”, Vychisl. tekhnologii, 11:2 (2006), 82–92 | Zbl

[10] G. V. Demidenko, S. V. Uspenskii, Partial differential equations and systems not solvable with respect to the highest-order derivative, Marcel Dekker, Inc., N. Y.–Basel–Hong Kong, 2003, 239 pp. | MR | Zbl

[11] A. Favini, A. Yagi, Degenerate differential equations in Banach spaces, Marcel Dekker, Inc., N. Y.–Basel–Hong Kong, 1999, 236 pp. | MR | Zbl

[12] Pazy A. A. Pazy, Semigroups of linear operators and applications to partial differential equations, Springer-Verlag, N.Y., 1983, 446 pp. | MR | Zbl

[13] S. G. Pyatkov, Operator theory. Nonclassical problems, VSP, Utrecht–Boston–Köln–Tokyo, 2002, 353 pp. | MR | Zbl

[14] N. Sidorov, B. Loginov, A. Sinithyn, M. Falaleev, Lyapunov–Schmidt methods in nonlinear analysis and applications, Kluwer Academic Publishers, Dordrecht–Boston–London, 2002, 548 pp. | MR | Zbl

[15] G. A. Sviridyuk, V. E. Fedorov, Linear Sobolev Type Equations and Degenerate Semigroups of Operators, VSP, Utrecht–Boston, 2003, 216 pp. | MR | Zbl