Geodesic
The continuous spectrum and the effect of parametric resonance. The case of bounded operators
Sbornik. Mathematics, Tome 205 (2014) no. 5, pp. 684-702 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper is concerned with the Mathieu-type differential equation $u''=-A^2 u+\varepsilon B(t)u$ 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 $\varepsilon$ and hence free of parametric resonance. Bibliography: 10 titles.
Keywords: parametric resonance, continuous spectrum, stability. 
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V. V. Skazka. The continuous spectrum and the effect of parametric resonance. The case of bounded operators. Sbornik. Mathematics, Tome 205 (2014) no. 5, pp. 684-702. http://geodesic.mathdoc.fr/item/SM_2014_205_5_a4/

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