Investigation of solvability of the nonlinear equilibrium problem of a shallow unfixed shell
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 3, pp. 105-110 Cet article a éte moissonné depuis la source Math-Net.Ru

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We deduce sufficient conditions for the solvability of the variational equilibrium problem of a shallow shell with free edges within the geometrically and physically nonlinear model of middle bending.
Keywords: shallow shell, geometrically nonlinear theory of middle bending, variational problem, solvability conditions.
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M. M. Karchevsky. Investigation of solvability of the nonlinear equilibrium problem of a shallow unfixed shell. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 3, pp. 105-110. http://geodesic.mathdoc.fr/item/UZKU_2013_155_3_a10/

[1] Vorovich I. I., Matematicheskie problemy nelineinoi teorii pologikh obolochek, Nauka, M., 1989, 373 pp. | MR

[2] Bernadou M., Oden J. T., “An existence theorem for a class of nonlinear shallow shell problems”, J. Math. Pures Appl., 60:3 (1981), 285–308 | MR | Zbl

[3] Karchevskii M. M., “O razreshimosti variatsionnykh zadach nelineinoi teorii pologikh obolochek”, Differents. uravneniya, 27:7 (1991), 1996–1203 | MR

[4] Karchevskii M. M., “O razreshimosti geometricheski nelineinykh zadach teorii tonkikh obolochek”, Izv. vuzov. Matem., 1995, no. 6, 30–36 | MR | Zbl

[5] Timergaliev S. N., Teoremy suschestvovaniya v nelineinoi teorii tonkikh uprugikh obolochek, Dis. $\dots$ d-ra fiz.-matem. nauk, Kazan, 2003, 340 pp.

[6] Timergaliev S. N., “K voprosu o razreshimosti kraevykh zadach nelineinoi teorii pologikh obolochek tipa Timoshenko”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 150, no. 1, 2008, 115–123 | Zbl

[7] Timergaliev S. N., “O razreshimosti geometricheski nelineinykh kraevykh zadach dlya anizotropnykh obolochek tipa Timoshenko s zhestko zadelannymi krayami”, Izv. vuzov. Matem., 2011, no. 8, 56–68 | MR | Zbl

[8] Mushtari Kh. M., Galimov K. Z., Nelineinaya teoriya uprugikh obolochek, Tatknigoizdat, Kazan, 1957, 432 pp.

[9] Fikera G., Teoremy suschestvovaniya v teorii uprugosti, Mir, M., 1974, 160 pp.

[10] Vainberg M. M., Variatsionnyi metod i metod monotonnykh operatorov, Nauka, M., 1972, 416 pp. | MR

[11] Kondratev V. A., Oleinik O. A., “Kraevye zadachi dlya sistemy uravnenii teorii uprugosti v neogranichennykh oblastyakh. Neravenstva Korna”, Usp. matem. nauk, 43:5 (1988), 55–98 | MR | Zbl

[12] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, M., 1977, 744 pp. | MR