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Strong nonresonance of Schrödinger operators and an averaging theorem. (English) Zbl 0885.35119

Summary: We prove that linear Schrödinger operators \(-\Delta+q\) on a torus or on a bounded smooth domain in \(\mathbb{R}^d\) 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-Bogolubov averaging theorem holds for nonlinear perturbations of the corresponding Schrödinger evolution equations.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35J10 Schrödinger operator, Schrödinger equation
35P20 Asymptotic distributions of eigenvalues in context of PDEs
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