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 Izv. Vyssh. Uchebn. Zaved. Mat., 2017, Number 10, Pages 38–49 (Mi ivm9288)

Linear differential second-order equations in Banach space and splitting of operators

A. G. Baskakov, T. K. Katsaran, T. I. Smagina

Voronezh State University, 1 University Sq., Voronezh, 394006, Russia

Abstract: We consider a linear differential second order equation in complex Banach space with bounded operator coefficients. We study the question of existence of bounded on the whole real axis solutions (with bounded right-hand side) and their asymptotic behaviour. The research is conducted in case of separated roots of the corresponding algebraic operator equation or providing that the norm of operator, placed in front of the first derivative in the equation, is small. In the latter case we apply the method of similar operators (operator splitting theorem). The main results are obtained with the use of the theorems on similarity transformation of second order operator matrix to a block-diagonal one.

Keywords: Banach space, differential second-order equation, the method of similar operators, operators splitting.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 1.3464.2017/4.6

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:10, 32–43

Bibliographic databases:

UDC: 517.983

Citation: A. G. Baskakov, T. K. Katsaran, T. I. Smagina, “Linear differential second-order equations in Banach space and splitting of operators”, Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 10, 38–49; Russian Math. (Iz. VUZ), 61:10 (2017), 32–43

Citation in format AMSBIB
\Bibitem{BasKatSma17} \by A.~G.~Baskakov, T.~K.~Katsaran, T.~I.~Smagina \paper Linear differential second-order equations in Banach space and splitting of operators \jour Izv. Vyssh. Uchebn. Zaved. Mat. \yr 2017 \issue 10 \pages 38--49 \mathnet{http://mi.mathnet.ru/ivm9288} \transl \jour Russian Math. (Iz. VUZ) \yr 2017 \vol 61 \issue 10 \pages 32--43 \crossref{https://doi.org/10.3103/S1066369X1710005X} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000413671000005} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85030853524} 

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• http://mi.mathnet.ru/eng/ivm/y2017/i10/p38

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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. A. V. Glushak, “Criterion for the solvability of the weighted Cauchy problem for an abstract Euler-Poisson-Darboux equation”, Differ. Equ., 54:5 (2018), 622–632
2. A. G. Baskakov, L. Yu. Kabantsova, T. I. Smagina, “Invertibility conditions for second-order differential operators in the space of continuous bounded functions”, Differ. Equ., 54:3 (2018), 285–294
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