Journal
SBORNIK MATHEMATICS
Volume 205, Issue 5, Pages 684-702Publisher
TURPION LTD
DOI: 10.1070/SM2014v205n05ABEH004394
Keywords
parametric resonance; continuous spectrum; stability
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Funding
- Presidium of the Russian Academy of Sciences (Fundamental Research Programme) [15]
- Siberian Branch of the Russian Academy of Sciences (Interdisciplinary Integration Projects) [30, 130]
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The paper is concerned with the Mathieu-type differential equation u '' = -A(2)u + epsilon B(t)u in a Hilbert space H. It is assumed that A is a bounded self-adjoint operator which only has an absolutely continuous spectrum and B(t) is almost periodic operator-valued function. Sufficient conditions are obtained under which the Cauchy problem for this equation is stable for small e and hence free of parametric resonance.
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