A. R. Aliev, S. S. Mirzoev, “On Boundary Value Problem Solvability Theory for a Class of High-Order Operator-Differential Equations”, Funktsional. Anal. i Prilozhen., 44:3 (2010), 63–65; Funct. Anal. Appl., 44:3 (2010), 209

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Funktsional'nyi Analiz i ego Prilozheniya, 2010, Volume 44, Issue 3, Pages 63–65
DOI: https://doi.org/10.4213/faa2996 (Mi faa2996)

This article is cited in 17 scientific papers (total in 17 papers)

Brief communications

On Boundary Value Problem Solvability Theory for a Class of High-Order Operator-Differential Equations

A. R. Aliev^ab, S. S. Mirzoev^a

^a Baku State University
^b Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences

Full-text PDF (158 kB) Citations (17)

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DOI: https://doi.org/10.4213/faa2996

Abstract: In this note, we establish sufficient conditions for the correct and unique solvability of various boundary value problems for a class of even-order operator-differential equations on the half-axis. These conditions are unimprovable in terms of operator coefficients of the equation. We note that the principal part of the equation under study suffers a discontinuity.

Keywords: Hilbert space, self-adjoint operator, operator-differential equation, discontinuous coefficient, regular solution, isomorphism, intermediate derivatives.

Received: 15.04.2009

English version:
Functional Analysis and Its Applications, 2010, Volume 44, Issue 3, Pages 209–211
DOI: https://doi.org/10.1007/s10688-010-0025-y

Bibliographic databases:

Document Type: Article

UDC: 517.946

Language: Russian

Citation: A. R. Aliev, S. S. Mirzoev, “On Boundary Value Problem Solvability Theory for a Class of High-Order Operator-Differential Equations”, Funktsional. Anal. i Prilozhen., 44:3 (2010), 63–65; Funct. Anal. Appl., 44:3 (2010), 209–211

Citation in format AMSBIB

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https://doi.org/10.4213/faa2996

https://www.mathnet.ru/eng/faa/v44/i3/p63

This publication is cited in the following 17 articles:

Kalemkush U.O., “On a Boundary Value Problem For Fourth-Order Operator-Differential Equations With a Variable Coefficient”, Azerbaijan J. Math., 10:1 (2020), 181–192
Mirzoev S.S., Rustamova L.A., “On a Boundary Value Problem For Second Order Operator Differential Equations”, Proceedings of the7Th International Conference on Control and Optimization With Industrial Applications, Vol. 1, eds. Fikret A., Tamer B., Baku State Univ, Inst Applied Mathematics, 2020, 287–289
Gesztesy F., Naboko S.N., Weikard R., Zinchenko M., “Donoghue-Type M-Functions For Schrodinger Operators With Operator-Valued Potentials”, J. Anal. Math., 137:1 (2019), 373–427
Aliev A.R., Soylemezo M.A., “Solvability Conditions in Weighted Sobolev Type Spaces For One Class of Inverse Parabolic Operator-Differential Equations”, Azerbaijan J. Math., 9:1 (2019), 59–75
Aliev A.R., Mirzoev S.S., Soylemezo M.A., “On Solvability of Third-Order Operator Differential Equation With Parabolic Principal Part in Weighted Space”, J. Funct. space, 2017, 2932134
N. N. Shadrina, “O vliyanii parametrov na razreshimost nekotorykh zadach sopryazheniya dlya ellipticheskikh uravnenii”, Sib. elektron. matem. izv., 13 (2016), 411–425
Mirzoev S.S., Aliev A.R., Gasimova G.M., “Solvability conditions of a boundary value problem with operator coefficients and related estimates of the norms of intermediate derivative operators”, Dokl. Math., 94:2 (2016), 566–568
Al-Aidarous E.S., Aliev A.R., Rzayev E.S., Zedan H.A., “Fourth Order Elliptic Operator-Differential Equations With Unbounded Operator Boundary Conditions in the Sobolev-Type Spaces”, Bound. Value Probl., 2015, 191
Aliev A.R., Elbably A.L., “on a Class of Operator-Differential Equations of the Third Order With Multiple Characteristics on the Whole Axis in the Weighted Space”, Math. Slovaca, 65:3 (2015), 667–682
Z.F. El-Raheem, A.H. Nasser, “On the spectral investigation of the scattering problem for some version of one-dimensional Schródinger equation with turning point”, Bound. Value Probl., 2014, 97, 12 pp.
S. S. Mirzoev, A. R. Aliev, L. A. Rustamova, “On the Boundary Value Problem with the Operator in Boundary Conditions for the Operator-Differential Equation of Second Order with Discontinous Coefficients”, Zhurn. matem. fiz., anal., geom., 9:2 (2013), 207–226
K. A. Kerimov, S. S. Mirzoyev, “On a Problem for Operator-Differential Second-Order Equations with Nonlocal Boundary Condition”, Math. Notes, 94:3 (2013), 330–334
Gesztesy F., Weikard R., Zinchenko M., “On Spectral Theory for Schrodinger Operators with Operator-Valued Potentials”, J. Differ. Equ., 255:7 (2013), 1784–1827
Gesztesy F., Weikard R., Zinchenko M., “Initial Value Problems and Weyl-Titchmarsh Theory for Schrodinger Operators with Operator-Valued Potentials”, Oper. Matrices, 7:2 (2013), 241–283
Aliev A.R., Elbably A.L., “Well-Posedness of a Boundary Value Problem for a Class of Third-Order Operator-Differential Equations”, Bound. Value Probl., 2013, 140
S. S. Mirzoev, I. Dzh. Dzhafarov, “On the Solvability of a Boundary-Value Problem for Second-Order Partial Differential Operator Equations”, Math. Notes, 91:3 (2012), 445–448
S. S. Mirzoyev, A. R. Aliev, L. A. Rustamova, “Solvability Conditions for Boundary-Value Problems for Elliptic Operator-Differential Equations with Discontinuous Coefficient”, Math. Notes, 92:5 (2012), 722–726

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

Functional Analysis and Its Applications

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