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On the behavior at infinity of solutions to differential equations in Hilbert spaces

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Abstract

The paper deals with the operator differential equation y(2n)(t)+Ay(n)(t)+By(t)=0, where A and B are self-adjoint commuting operators, in a Hilbert space. Criteria are established for stability and stabilization of solutions at infinity. In the case of growing solutions, their asymptotic behavior is investigated. Examples are given from mathematical physics. Bibliography: 21 titles.

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Authors
  1. M. L. Gorbachuk
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  2. A. Ya. Shklyar
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Additional information

Dedicated to Olga Arsenievna Oleinik as a token of acknowledgment for her outstanding role in the development of the theory of differential equations

Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 19, pp. 000-000, 0000

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Gorbachuk, M.L., Shklyar, A.Y. On the behavior at infinity of solutions to differential equations in Hilbert spaces. J Math Sci 85, 2347–2362 (1997). https://doi.org/10.1007/BF02355842

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  • DOI: https://doi.org/10.1007/BF02355842

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