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 Mat. Zametki, 2012, Volume 91, Issue 6, Pages 861–869 (Mi mz9389)

On the Solvability of the Boundary-Value Problem for Second-Order Equations in Hilbert Space with an Operator Coefficient in the Boundary Condition

S. S. Mirzoevab, M. Yu. Salimova

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

Abstract: We consider the boundary-value problem on a finite interval for a class of second-order operator-differential equations with a linear operator in one of its boundary conditions. We obtain sufficient conditions for the regular solvability of the boundary-value problem under consideration; these conditions are expressed only in terms of its operator coefficients.

Keywords: second-order operator-differential equation, boundary-value problem, Hilbert space, self-adjoint operator, square-integrable function, linear bounded operator, Banach inverse-operator theorem

DOI: https://doi.org/10.4213/mzm9389

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English version:
Mathematical Notes, 2012, 91:6, 808–815

Bibliographic databases:

UDC: 517.96+517.43

Citation: S. S. Mirzoev, M. Yu. Salimov, “On the Solvability of the Boundary-Value Problem for Second-Order Equations in Hilbert Space with an Operator Coefficient in the Boundary Condition”, Mat. Zametki, 91:6 (2012), 861–869; Math. Notes, 91:6 (2012), 808–815

Citation in format AMSBIB
\Bibitem{MirSal12} \by S.~S.~Mirzoev, M.~Yu.~Salimov \paper On the Solvability of the Boundary-Value Problem for Second-Order Equations in Hilbert Space with an Operator Coefficient in the Boundary Condition \jour Mat. Zametki \yr 2012 \vol 91 \issue 6 \pages 861--869 \mathnet{http://mi.mathnet.ru/mz9389} \crossref{https://doi.org/10.4213/mzm9389} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3201523} \elib{http://elibrary.ru/item.asp?id=20731552} \transl \jour Math. Notes \yr 2012 \vol 91 \issue 6 \pages 808--815 \crossref{https://doi.org/10.1134/S0001434612050276} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000305984400027} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84864218665} 

• http://mi.mathnet.ru/eng/mz9389
• https://doi.org/10.4213/mzm9389
• http://mi.mathnet.ru/eng/mz/v91/i6/p861

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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. 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
2. A. R. Aliev, N. L. Muradova, “Third-order operator-differential equations with discontinuous coefficients and operators in the boundary conditions”, Electron. J. Differ. Equ., 2013, 219
3. E. S. Al-Aidarous, A. R. Aliev, E. S. Rzayev, H. A. Zedan, “Fourth order elliptic operator-differential equations with unbounded operator boundary conditions in the Sobolev-type spaces”, Bound. Value Probl., 2015, 191
4. S. S. Mirzoyev, H. I. Zamanov, “On multiple completeness of eigen and associated vectors of a class of operator pencils”, Proc. Inst. Math. Mech., 43:2 (2017), 188–196
5. Mirzoyev S.S., Babayeva S.F., “On Completeness of a Part of Eigen and Associated Vectors of a Quadratic Operator Pencil For a Double-Point Boundary Value Problem”, TWMS J. Pure Appl. Math., 10:1 (2019), 83–93
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