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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{SM_2014_205_5_a4,
     author = {V. V. Skazka},
     title = {The continuous spectrum and the effect of parametric resonance. {The} case of bounded operators},
     journal = {Sbornik. Mathematics},
     pages = {684--702},
     publisher = {mathdoc},
     volume = {205},
     number = {5},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2014_205_5_a4/}
}
TY  - JOUR
AU  - V. V. Skazka
TI  - The continuous spectrum and the effect of parametric resonance. The case of bounded operators
JO  - Sbornik. Mathematics
PY  - 2014
SP  - 684
EP  - 702
VL  - 205
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2014_205_5_a4/
LA  - en
ID  - SM_2014_205_5_a4
ER  - 
%0 Journal Article
%A V. V. Skazka
%T The continuous spectrum and the effect of parametric resonance. The case of bounded operators
%J Sbornik. Mathematics
%D 2014
%P 684-702
%V 205
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2014_205_5_a4/
%G en
%F SM_2014_205_5_a4
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/