Kappeler, T; Kuksin, S (1995). Strong nonresonance of Schrödinger operators and an averaging theorem. Physica D: Nonlinear Phenomena, 86(3):349-362.
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.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > Statistical and Nonlinear Physics
Physical Sciences > Mathematical Physics Physical Sciences > Condensed Matter Physics Physical Sciences > Applied Mathematics |
| Language: | English |
| Date: | 1995 |
| Deposited On: | 29 Nov 2010 16:28 |
| Last Modified: | 29 Jul 2020 19:49 |
| Publisher: | Elsevier |
| ISSN: | 0167-2789 |
| OA Status: | Closed |
| 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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Kappeler, T