# Correction to: Long time dynamics for semi-relativistic NLS and half wave in arbitrary dimension (Mathematische Annalen, (2018), 371, 1-2, (707-740), 10.1007/s00208-018-1666-z)

Jacopo Bellazzini, Vladimir Georgiev, Nicola Visciglia

1 被引用数 (Scopus)

## 抄録

The assumptions of Theorem 1.2 are not correct in case n = 1. In dimension n = 1, instead of 1+ 2 n ˂ p ˂ 1+ 2 n-1 it is correct 3 ˂ p ˂ 5. Indeed the scaling argument in Proposition 3.1 works only if 3 ˂ p ˂ 5. The correct Theorem is now the following: Theorem 1.2 Let 3 ˂ p ˂ 5 if n = 1 and 1+ 2 n ˂ p ˂ 1+ 2 n-1 if n = 2. There exists r0 ˃ 0 such that the following conditions occur for every r ? (0, r0): • Jr ˃ -8, Br = Ø and Br ? B1/2 n H1(Rn), where Br := {v ? Sr n B1 s.t. Es(v) = Jr }. In particular for every v ? Br there exists ? ? R such that v 1 - v + ?v - v|v|p-1 = 0;.

本文言語 English 1795-1796 2 Mathematische Annalen 376 3-4 https://doi.org/10.1007/s00208-020-01972-z Published - 2020 4 1

• 数学 (全般)

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