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Mat. Sb. (N.S.), 1981, Volume 115(157), Number 3(7), Pages 323–336 (Mi msb2398)  

This article is cited in 19 scientific papers (total in 21 papers)

Degenerate operator equations

A. A. Dezin


Abstract: The differential-operator equation
$$ [-D_tt^\alpha D_t-D_tA-P]u=f $$
is studied, where $D_t\equiv\frac d{dt}$, $t\in[0,b]$, $\alpha\geqslant0$, and the operators $A,P\colon\mathscr H\to\mathscr H$, which commute with $D_t$, act in a Hilbert space $\mathscr H$ and satisfy appropriate (quite strong) requirements formulated in terms of resolvent, or spectral, properties. The character of the boundary conditions with respect to $t$ (at $t=0,b$), which are imposed on the equation and ensure existence and uniqueness of the solution, is elucidated, and properties of the solution depending on $\alpha$ and on the properties of the operators $A$ and $P$ are investigated, as well.
Bibliography: 7 titles.

Full text: PDF file (1332 kB)
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English version:
Mathematics of the USSR-Sbornik, 1982, 43:3, 287–298

Bibliographic databases:

UDC: 517.944
MSC: 35R20
Received: 16.12.1980

Citation: A. A. Dezin, “Degenerate operator equations”, Mat. Sb. (N.S.), 115(157):3(7) (1981), 323–336; Math. USSR-Sb., 43:3 (1982), 287–298

Citation in format AMSBIB
\Bibitem{Dez81}
\by A.~A.~Dezin
\paper Degenerate operator equations
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 115(157)
\issue 3(7)
\pages 323--336
\mathnet{http://mi.mathnet.ru/msb2398}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=628214}
\zmath{https://zbmath.org/?q=an:0501.35073|0473.35074}
\transl
\jour Math. USSR-Sb.
\yr 1982
\vol 43
\issue 3
\pages 287--298
\crossref{https://doi.org/10.1070/SM1982v043n03ABEH002449}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Maksudov F., Shakhmurov V., “On the Completeness of the System of the Eigen and Attached Vectors of the Nonlocal Boundary-Value-Problems for the Quasi-Elliptic Partial-Differential Operator-Equations”, 268, no. 1, 1983, 33–35  mathscinet  zmath  isi
    2. V. B. Shakhmurov, “Imbedding theorems for abstract function spaces and their applications”, Math. USSR-Sb., 62:1 (1989), 261–276  mathnet  crossref  mathscinet  zmath
    3. Tepoyan L., “Singular 4th-Order Differential-Operational Equations”, Differ. Equ., 23:8 (1987), 930–939  mathscinet  zmath  isi
    4. Shakhmurov V., “Imbedding Theorems and their Applications to Degenerate Equations”, Differ. Equ., 24:4 (1988), 475–482  mathnet  mathscinet  zmath  isi
    5. Yataev N., “Degenerate 3rd-Order Differential-Operational Equations”, Differ. Equ., 24:3 (1988), 340–344  mathnet  mathscinet  zmath  isi
    6. Shakhmurov V., Babayev A., “Coercive Problems for Equation with Parameters”, 315, no. 1, 1990, 37–40  mathscinet  zmath  isi
    7. Sabziev E., “Weighted Boundary-Value-Problems for Strongly Degenerate Equations”, Differ. Equ., 28:12 (1992), 1813–1815  mathnet  mathscinet  zmath  isi
    8. N. M. Yataev, “Unique solvability of certain boundary-value problems for degenerate third order operational equations”, Math. Notes, 54:1 (1993), 754–763  mathnet  crossref  mathscinet  zmath  isi  elib
    9. Sabziev E., “The Weight Dirichlet Problem for a Strongly Degenerate Ordinary Equation”, Differ. Equ., 31:4 (1995), 675–679  mathnet  mathscinet  zmath  isi
    10. V. V. Kornienko, “On the spectra of first order irregular operator equations”, Sb. Math., 188:8 (1997), 1213–1234  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. Kornienko V., “For Spectrum of Irregular Differential Equation”, Dokl. Akad. Nauk, 361:1 (1998), 10–13  mathnet  mathscinet  zmath  isi
    12. Dzhabrailov M., “On Coercive Solvability of Differential-Operator Equations in Besov Type Spaces”, Dokl. Akad. Nauk, 359:3 (1998), 301–303  mathnet  mathscinet  zmath  isi
    13. V. V. Kornienko, “On the Spectrum of Degenerate Operator Equations”, Math. Notes, 68:5 (2000), 576–587  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    14. V. S. Vladimirov, I. V. Volovich, A. K. Gushchin, Yu. N. Drozhzhinov, V. V. Zharinov, B. I. Zav'yalov, V. A. Il'in, G. I. Marchuk, V. P. Mikhailov, E. I. Moiseev, S. M. Nikol'skii, B. V. Pal'tsev, “Aleksei Alekseevich Dezin (obituary)”, Russian Math. Surveys, 64:3 (2009), 553–560  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    15. M. K. Kerimov, B. V. Pal'tsev, “In Memory of Professor Aleksei Alekseevich Dezin (1923–2008)”, Comput. Math. Math. Phys., 49:2 (2009), 387–390  mathnet  crossref  mathscinet  isi  elib
    16. L. P. Tepoyan, Kalvand Daryoush, “Neumann problem for fourth order degenerate ordinary differential equations”, Uch. zapiski EGU, ser. Fizika i Matematika, 2010, no. 1, 22–26  mathnet
    17. Esmail Yousefi, “A mixed problem for the fourth order degenerate ordinary differential equation”, Uch. zapiski EGU, ser. Fizika i Matematika, 2010, no. 2, 16–19  mathnet
    18. Hosein Ansari, “Degenerate differential-operator equations on infinite interval”, Uch. zapiski EGU, ser. Fizika i Matematika, 2011, no. 2, 27–32  mathnet
    19. L. Tepoyan, “DEGENERATE DIFFERENTIAL-OPERATOR EQUATIONS OF HIGHER ORDER AND ARBITRARY WEIGHT”, Asian-European J. Math, 05:02 (2012), 1250030  crossref
    20. L. P. Tepoyan, H. S. Grigoryan, “On degenerate nonself-adjoint differential equations of fourth order”, Uch. zapiski EGU, ser. Fizika i Matematika, 2012, no. 3, 29–33  mathnet
    21. L. Tepoyan, “Degenerate differential-operator equations on infinite intervals”, J Math Sci, 189:1 (2013), 164  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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