Geodesic
On the asymptotics of solutions of differential equations in Hilbert space
Sbornik. Mathematics, Tome 72 (1992) no. 2, pp. 485-501 Cet article a éte moissonné depuis la source Math-Net.Ru

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Solutions of differential equations of first and arbitrary order in Hilbert space are investigated; they arise in the study of elliptic problems in cylindrical domains and in domains with singular points. Existence theorems are obtained for a broad class of right sides, and the asymptotics of a solution as $t\to\infty$ is constructed under “minimal” conditions on the coefficients. The results make considerable progress possible in the study of qualitative properties of solutions of elliptic equations of higher order. 
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L. A. Bagirov; V. A. Kondrat'ev. On the asymptotics of solutions of differential equations in Hilbert space. Sbornik. Mathematics, Tome 72 (1992) no. 2, pp. 485-501. http://geodesic.mathdoc.fr/item/SM_1992_72_2_a12/

[1] Lax P. D., “A Phragmen - Lindelöf theorem in harmonic analysis and its application to some questions on the theory of elliptic equations”, Comm. Pure. Appl. Math., 10 (1957), 361–389 | DOI | MR | Zbl

[2] Evgrafov M. A., “Struktura reshenii eksponentsialnogo rosta dlya nekotorykh operatornykh uravnenii”, Tr. MIAN, 60 (1961), 145–180 | MR | Zbl

[3] Agmon S., Nirenberg L., “Properties of solutions of ordinary differential equations in Banach spaces”, Comm. Pure Appl. Math., 16 (1963), 121–239 | DOI | MR | Zbl

[4] Pazy A., “Asymptotic expansions of solutions of ordinary differential equations in Hilbert space”, Arch. Rat. Mech. and Anal., 24:3 (1969), 193–218 | DOI | MR

[5] Kondratev V. A., “Kraevye zadachi dlya ellipticheskikh uravnenii v oblastyakh s konicheskimi ili uglovymi tochkami”, Tr. MMO, 16, 1967, 209–292

[6] Mazya V. G., Plamenevskii B. A., “Ob asimptoticheskom povedenii reshenii differentsialnykh uravnenii v gilbertovom prostranstve”, Izv. AN SSSR. Ser. matem., 36 (1972), 1080–1133

[7] Bagirov L. A., Kondratev V. A., “O regulyarnosti reshenii ellipticheskikh uravnenii vysokogo poryadka s nepreryvnymi koeffitsientami”, UMN, 44:1 (1989), 185–186 | MR | Zbl

[8] Kozlov V. A., Mazya V. G., “Otsenki $L_p$-srednikh i asimptotika reshenii ellipticheskikh kraevykh zadach v konuse. II: Operatory s peremennymi koeffitsientami”, Math. Nachr., 137 (1988), 113–139 | DOI | MR | Zbl

[9] Gokhberg I. Ts., Krein M. G., “Osnovnye polozheniya o defektnykh chislakh, kornevykh chislakh i indeksakh lineinykh operatorov”, UMN, 12:2 (1957), 44–118 | MR

[10] Blekher P. M., “Ob operatorakh, zavisyaschikh meromorfno ot parametra”, Vestn. MGU. Ser. matem., mekh., 1969, no. 5, 30–36 | Zbl

[11] Yakovlev G. N., “Granichnye svoistva funktsii klassa $W_p^l$ na oblastyakh s uglovymi tochkami”, DAN SSSR, 140:1 (1961), 73–76 | MR | Zbl

[12] Solonnikov V. A., “Apriornye otsenki dlya uravnenii vtorogo poryadka parabolicheskogo tipa”, Tr. MIAN, 70, 1964, 133–212 | MR | Zbl