Dispersive estimates for Schrödinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three: II

被引：0

作者：

Erdoǧan M.B. ^{[1
]}

Schlag W. ^{[2
]}

机构：

[1] Department of Mathematics, University of Illinois, Urbana

[2] Department of Mathematics, University of Chicago, Chicago, IL 60637

来源：

Journal d’Analyse Mathématique | 2006年 / 99卷 / 1期

基金：

美国国家科学基金会;

关键词：

Solitary Wave; Standing Wave; Discrete Spectrum; Essential Spectrum; Neumann Series;

D O I：

10.1007/BF02789446

中图分类号：

学科分类号：

摘要：

We investigate boundedness of the evolution eitH in the sense of L2(ℝ3) → L2(ℝ3) as well as L1(ℝ3) → L∞(ℝ 3) for the non-selfadjoint operator H = [V2 -Δ+μ-V1Δ - μ +V1-V2 where μ > 0 and V1, V2 are real-valued decaying potentials. Such operators arise when linearizing a focusing NLS equation around a standing wave, and the aforementioned bounds are needed in the study of nonlinear asymptotic stability of such standing waves. We derive our results under some natural spectral assumptions (corresponding to a ground state soliton of NLS), see A1)-A4) below, but without imposing any restrictions on the edges ±μ of the essential spectrum. Our goal is to develop an "axiomatic approach," which frees the linear theory from any nonlinear context in which it may have arisen.

引用

页码：199 / 249

页数：50

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