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Sibirskii Matematicheskii Zhurnal, 2010, Volume 51, Number 4, Pages 815–828 (Mi smj2127)  
This article is cited in 5 scientific papers (total in 5 papers)

Completeness of elementary solutions to a class of second order operator-differential equations

S. S. Mirzoevab, M. Yu. Salimova

a Baku State University, Baku, Azerbaijan
b Institute of Mathematics and Mechanics of the NAS of Azerbaijan and Baku State University, Baku, Azerbaijan
Full-text PDF (304 kB) Citations (5)
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Abstract: We present conditions of solvability of a boundary value problem for a class of second order operator-differential equations on a finite segment, study the behavior of the resolvent of the corresponding operator pencil, prove the double completeness of a system of the derived chains of eigenvectors and associated vectors corresponding to a boundary value problem on a segment, and establish the completeness of elementary solutions to the homogeneous equation in the solution space.
Keywords: boundary value problem, operator-differential equation, Hilbert space, selfadjoint operator, eigenvectors and associated vectors, resolvent.
Received: 21.01.2009
English version:
Siberian Mathematical Journal, 2010, Volume 51, Issue 4, Pages 648–659
DOI: https://doi.org/10.1007/s11202-010-0066-8
Bibliographic databases:
Document Type: Article
UDC: 517.43+517.946
Language: Russian
Citation: S. S. Mirzoev, M. Yu. Salimov, “Completeness of elementary solutions to a class of second order operator-differential equations”, Sibirsk. Mat. Zh., 51:4 (2010), 815–828; Siberian Math. J., 51:4 (2010), 648–659
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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