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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry], 2006, Volume 2, Number 4, Pages 347–357 (Mi jmag40)  
This article is cited in 1 scientific paper (total in 1 paper)

On the solvability of a class of operator differential equations of the second order on the real axis

A. R. Alievab

a Baku State University, 23 Z. Khalilov Str., Baku, AZ-1148, Azerbaijan
b Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 9 F. Agaev Str., Baku, AZ-1141, Azerbaijan
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Abstract: Solvability of the operator dierential equation of the second order with variable coefficients on the real axis in a certain weight space is studied. The main part of the equation is an abstract elliptic equation in Hilbert space. We note that sufficient conditions on operator coefficients of the perturbed part, preserving ellipticity of the equation, are found in the paper, and estimations of the norms of intermediate derivative operators via the main part of the operator differential equation in a certain weight space are also obtained.
Key words and phrases: operator diffeerential equation, selfadjoint operator, discontinuous coefficient, regular solution, Hilbert space.
Received: 15.12.2005
Bibliographic databases:
Document Type: Article
MSC: 47E05, 34B05
Language: English
Citation: A. R. Aliev, “On the solvability of a class of operator differential equations of the second order on the real axis”, Zh. Mat. Fiz. Anal. Geom., 2:4 (2006), 347–357
Citation in format AMSBIB
\Bibitem{Ali06}
\by A.~R.~Aliev
\paper On the solvability of a class of operator differential equations of the second order on the real axis
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2006
\vol 2
\issue 4
\pages 347--357
\mathnet{http://mi.mathnet.ru/jmag40}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2278868}
\zmath{https://zbmath.org/?q=an:1159.34044}
\elib{https://elibrary.ru/item.asp?id=12928615}
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    • This publication is cited in the following 1 articles:
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