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Strong nonresonance of Schrödinger operators and an averaging theorem


Kappeler, T; Kuksin, S (1995). Strong nonresonance of Schrödinger operators and an averaging theorem. Physica D: Nonlinear Phenomena, 86(3):349-362.

Abstract

We prove that linear Schrödinger operators −Δ+q on a torus or on a bounded smooth domain in Rd, considered with Dirichlet boundary conditions, have a strongly nonresonant spectrum for any potential q of generic type (generic in the sense of Kolmogorov measure). As a consequence, a Krylov-Bogolyubov averaging theorem holds for nonlinear perturbations of the corresponding Schrödinger evolution equations.

We prove that linear Schrödinger operators −Δ+q on a torus or on a bounded smooth domain in Rd, considered with Dirichlet boundary conditions, have a strongly nonresonant spectrum for any potential q of generic type (generic in the sense of Kolmogorov measure). As a consequence, a Krylov-Bogolyubov averaging theorem holds for nonlinear perturbations of the corresponding Schrödinger evolution equations.

Citations

2 citations in Web of Science®
3 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1995
Deposited On:29 Nov 2010 16:28
Last Modified:05 Apr 2016 13:27
Publisher:Elsevier
ISSN:0167-2789
Publisher DOI:https://doi.org/10.1016/0167-2789(95)00115-K
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0885.35119

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