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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2011, Number 6, Pages 21–26
(Mi vmumm731)
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This article is cited in 7 scientific papers (total in 7 papers)
Mathematics
Oscillation and wandering of solutions to a second order differential equation
I. N. Sergeev Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
The Lyapunov's oscillation and wandering characteristics of solutions to a second order linear equation are defined, namely, the mean frequency of a solution, of its derivative or their various linear combinations, the mean angular velocity of the vector composed of a solution and its derivative, also wandering indices derived from that velocity. Nearly all of the values introduced for any equation are proved to be the same: for the autonomic equation – just all (moreover they coincide with the modules of the imaginary parts of the roots of the characteristic polynomial), but even for the periodic one – generally speaking, not all.
Key words:
differential equation, zeros of solutions, oscillation and wandering, characteristic exponents.
Received: 08.12.2010
Citation:
I. N. Sergeev, “Oscillation and wandering of solutions to a second order differential equation”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2011, no. 6, 21–26
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https://www.mathnet.ru/eng/vmumm731 https://www.mathnet.ru/eng/vmumm/y2011/i6/p21
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Abstract page: | 85 | Full-text PDF : | 29 |
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