Erratum: Stabilization of solutions to nonlinear Schrödinger equations
Erratum: Stabilization of solutions to nonlinear Schrödinger equations
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勘误表：非线性薛定谔方程解的稳定性
DOI：
10.1002/cpa.20052
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发表时间：
2005
影响因子：
3
通讯作者：
S. Cuccagna
中科院分区：
文献类型：
--
作者：
S. Cuccagna
文献[1]中引理5.2的证明有几处错误。然而，这一说法是正确的，并且在本期杂志的[3，引理2.4]中得到了初步的证明，这一次是正确的。在[1]中的推论3.2的证明中，我们错误地引用了加藤关于微扰理论的教科书。事实上，如文献[1]所述，引理3.1推出的推论3.2是不正确的。然而，[1]的推论3.2是[2]中的命题3.1的结果，或者在更一般的假设下，允许将本征值嵌入到连续谱中，并且对于空间维度3，是[3]中的命题4.1。
The proof of lemma 5.2 in [1] contains several mistakes. Nevertheless, thestatement is correct and is proven in an elementary fashion, correctly this time, in[3, lemma 2.4], which is in this issue of the journal.In the proof of corollary 3.2 in [1], we misquoted from Kato’s textbook on per-turbation theory. In fact, it is not true that, as asserted in [1], corollary 3.2 followsfrom lemma 3.1. However, corollary 3.2 of [1] is a consequence of proposition 3.1in [2] or, under more general hypotheses that allow eigenvalues embedded in thecontinuous spectrum and for space dimension 3, proposition 4.1 in [3].