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.


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