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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 141, Pages 103–110
(Mi into247)
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This article is cited in 1 scientific paper (total in 1 paper)
On asymptotics of solutions to some linear differential equations
K. A. Mirzoeva, N. N. Konechnajab, T. A. Safonovab, R. N. Tagirovab a Lomonosov Moscow State University
b Northern (Arctic) Federal University named after M. V. Lomonosov, Arkhangelsk
Abstract:
In this paper, we find the principal asymptotic term at infinity of a certain fundamental system of solutions to the equation $l_{2n}[y]=\lambda y$ of order $2n$, where $l_{2n}$ is the product of second-order linear differential expressions and $\lambda$ is a fixed complex number. We assume that the coefficients of these differential expressions are not necessarily smooth but have a prescribed power growth at infinity. The asumptotic formulas obtained are applied for the problem on the defect index of differential operators in the case where $l_{2n}$ is a symmetric (formally self-adjoint) differential expression.
Keywords:
principal asymptotic term, quasi-derivative, product of quasi-differential expressions, differential operator, defect index.
Citation:
K. A. Mirzoev, N. N. Konechnaja, T. A. Safonova, R. N. Tagirova, “On asymptotics of solutions to some linear differential equations”, Differential equations. Spectral theory, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 141, VINITI, M., 2017, 103–110; Journal of Mathematical Sciences, 241:5 (2019), 614–621
Linking options:
https://www.mathnet.ru/eng/into247 https://www.mathnet.ru/eng/into/v141/p103
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Abstract page: | 235 | Full-text PDF : | 79 | First page: | 23 |
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