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Izv. Akad. Nauk SSSR Ser. Mat., 1972, Volume 36, Issue 5, Pages 1080–1133 (Mi izv2346)  

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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English version:
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
\Bibitem{MazPla72}
\by V.~G.~Maz'ya, B.~A.~Plamenevskii
\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
\mathnet{http://mi.mathnet.ru/izv2346}
\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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    Citing articles on Google Scholar: Russian citations, English citations
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    Erratum

    This publication is cited in the following articles:
    1. 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  mathnet  crossref  mathscinet  zmath
    2. B. A. Plamenevskii, “On the asymptotic behavior of solutions of quasielliptic differential equations with operator coefficients”, Math. USSR-Izv., 7:6 (1973), 1327–1370  mathnet  crossref  mathscinet  zmath
    3. 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  mathnet  crossref  mathscinet
    4. S. A. Nazarov, “Elliptic boundary value problems with periodic coefficients in a cylinder”, Math. USSR-Izv., 18:1 (1982), 89–98  mathnet  crossref  mathscinet  zmath  isi
    5. 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  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. 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  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. Bert-Wolfgang Schulze, Nikolai Tarkhanov, “Euler solutions of pseudodifferential equations”, Integr equ oper theory, 33:1 (1999), 98  crossref  mathscinet  zmath  isi
    8. S. A. Nazarov, A. S. Slutskii, “Saint-venant principle for paraboloidal elastic bodies”, Journal of Mathematical Sciences (New York), 98:6 (2000), 717  crossref  mathscinet  elib
    9. 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  crossref  mathscinet  zmath
    10. Ya. Rebahi, “Asymptotics of Sol tions of Differential Equations on Manifolds with Cusps”, Math Nachr, 236:1 (2002), 161  crossref  mathscinet  zmath
    11. 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  mathnet  crossref  mathscinet  elib
    12. S. A. Nazarov, “Concentration of trapped modes in problems of the linearized theory of water waves”, Sb. Math., 199:12 (2008), 1783–1807  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    13. 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  mathnet  crossref  mathscinet  isi  elib  elib
    14. 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  isi
    15. 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  crossref  elib
    16. 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  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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