Uniqueness and non-degeneracy of solutions for nonlinear fractional Schrödinger equation with perturbation

IF 1.2 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Journal of Mathematical Physics Pub Date : 2024-08-19 DOI:10.1063/5.0208876

Yuanda Wu, Yimin Zhang

引用次数: 0

Abstract

This paper concerned a fractional Schrödinger equation in whole space, for ɛ > 0 is a small parameter, ɛ2s(−Δ)su + V(x)u = |u|p−2u, where 12<s<1, N > 1 and 2<p<2NN−2s. We prove the non-degeneracy and uniqueness of bubble solutions by using local Pohozaev identity and finite dimensional reduction, which are the cornerstones to construct different type solutions.

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有扰动的非线性分式薛定谔方程解的唯一性和非退化性

本文涉及全空间的分薛定谔方程，对于ɛ > 0 是一个小参数，ɛ2s(-Δ)su + V(x)u = |u|p-2u，其中 12<s<1, N > 1 和 2<p<2NN-2s。我们利用局部 Pohozaev 特性和有限降维证明了气泡解的非退化性和唯一性，这是构建不同类型解的基石。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

2.20

自引率

15.40%

发文量

396

审稿时长

4.3 months

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