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This article is cited in 16 scientific papers (total in 16 papers)
On the asymptotic behavior of solutions of differential equations in Hilbert space
V. G. Maz'ya, B. A. Plamenevskii
Abstract:
Differential equations of arbitrary order with unbounded variable operator valued coefficients in a Hilbert space are considered. Asymptotic formulas for solutions are derived under the assumption that the coefficients are “weakly stabilized” at infinity.
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Mathematics of the USSR-Izvestiya, 1972, 6:5, 1067–1116
Bibliographic databases:
 
UDC:
517.9
MSC: Primary 35R20, 35B40, 34G05; Secondary 35B30, 35J40, 35K35
Received: 17.11.1971
Citation:
V. G. Maz'ya, B. A. Plamenevskii, “On the asymptotic behavior of solutions of differential equations in Hilbert space”, Izv. Akad. Nauk SSSR Ser. Mat., 36:5 (1972), 1080–1133; Math. USSR-Izv., 6:5 (1972), 1067–1116
Citation in format AMSBIB
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\paper On the asymptotic behavior of solutions of differential equations in Hilbert space
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1972
\vol 36
\issue 5
\pages 1080--1133
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=0352728}
\zmath{https://zbmath.org/?q=an:0266.34067}
\transl
\jour Math. USSR-Izv.
\yr 1972
\vol 6
\issue 5
\pages 1067--1116
\crossref{https://doi.org/10.1070/IM1972v006n05ABEH001912}
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Erratum
This publication is cited in the following articles:
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B. A. Plamenevskii, “On the existence and asymptotics of solutions of differential equations with unbounded operator coefficients in a Banach space”, Math. USSR-Izv., 6:6 (1972), 1327–1379
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B. A. Plamenevskii, “On the asymptotic behavior of solutions of quasielliptic differential equations with operator coefficients”, Math. USSR-Izv., 7:6 (1973), 1327–1370
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R. M. Yul'met'yev, “Bogolyubov's abridged description of equilibrium systems and derivation of an equation for the radial distribution function in a liquid”, Theoret. and Math. Phys., 25:2 (1975), 1100–1108
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S. A. Nazarov, “Elliptic boundary value problems with periodic coefficients in a cylinder”, Math. USSR-Izv., 18:1 (1982), 89–98
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L. A. Bagirov, V. A. Kondrat'ev, “On the regularity of solutions of elliptic equations of high order with continuous coefficients”, Russian Math. Surveys, 44:1 (1989), 233–234
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L. A. Bagirov, V. A. Kondrat'ev, “On the asymptotics of solutions of differential equations in Hilbert space”, Math. USSR-Sb., 72:2 (1992), 485–501
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Bert-Wolfgang Schulze, Nikolai Tarkhanov, “Euler solutions of pseudodifferential equations”, Integr equ oper theory, 33:1 (1999), 98
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S. A. Nazarov, A. S. Slutskii, “Saint-venant principle for paraboloidal elastic bodies”, Journal of Mathematical Sciences (New York), 98:6 (2000), 717
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Vladimir Rabinovich, Bert-Wolfgang Schulze, Nikolai Tarkhanov, “A Calculus of Boundary Value Problems in Domains with Non-Lipschitz Singula Points”, Math Nachr, 215:1 (2000), 115
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Ya. Rebahi, “Asymptotics of Sol tions of Differential Equations on Manifolds with Cusps”, Math Nachr, 236:1 (2002), 161
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V. V. Vlasov, D. A. Medvedev, “Functional-differential equations in Sobolev spaces and related problems of spectral theory”, Journal of Mathematical Sciences, 164:5 (2010), 659–841
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S. A. Nazarov, “Concentration of trapped modes in problems of the linearized theory of water waves”, Sb. Math., 199:12 (2008), 1783–1807
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F. L. Bakharev, S. A. Nazarov, “On the structure of the spectrum for the elasticity problem in a body with a supersharp spike”, Siberian Math. J., 50:4 (2009), 587–595
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Nazarov S.A. Sokolowski J. Taskinen J., “Neumann Laplacian on a Domain with Tangential Components in the Boundary”, Ann. Acad. Sci. Fenn. Ser. A1-Math., 34:1 (2009), 131–143
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O. Kiselev, I. Shestakov, “Asymptotics of solutions to the Laplace–Beltrami equation on a rotation surface with a cusp☆”, Journal of Mathematical Analysis and Applications, 362:2 (2010), 393
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Nazarov S.A. Taskinen J., “Spectral Anomalies of the Robin Laplacian in Non-Lipschitz Domains”, J. Math. Sci.-Univ. Tokyo, 20:1 (2013), 27–90
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