Izv. Vyssh. Uchebn. Zaved. Mat., 2017, Number 10, Pages 38–49
This article is cited in 2 scientific papers (total in 2 papers)
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
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.
Banach space, differential second-order equation, the method of similar operators, operators splitting.
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Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:10, 32–43
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
\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.
\jour Russian Math. (Iz. VUZ)
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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
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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