Nondegeneracy of nonradial sign-changing solutions to the nonlinear Schrödinger equation

Weiwei Ao; Monica Musso; Juncheng Wei

doi:10.24033/bsmf.2774

Nondegeneracy of nonradial sign-changing solutions to the nonlinear Schrödinger equation

Weiwei Ao, Monica Musso, Juncheng Wei

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that the non-radial sign-changing solutions to the nonlinear Schrödinger equation ∆u − u + |u|^p−¹u = 0 in R^N, u ∈ H¹ (R^N) constructed by Musso, Pacard, and Wei [16] are non-degenerate. This provides the first example of a non-degenerate sign-changing solution to the above nonlinear Schrödinger equation with finite energy.

Original language	English
Pages (from-to)	1-48
Number of pages	48
Journal	Bulletin de la Societe Mathematique de France
Volume	147
Issue number	1
DOIs	https://doi.org/10.24033/bsmf.2774
Publication status	Published - 31 Dec 2019

Bibliographical note

Funding Information:
The research of the second author has been supported in part by Fondecyt Grant 1160135 and Millennium Nucleus Center for Analysis of PDE, NC130017. The research of the third author is supported in part by NSERC of Canada.

Publisher Copyright:
© Société Mathématique de France

Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

Keywords

Orthogonality condition
Schrödinger equation
Sign-changing solution

ASJC Scopus subject areas

General Mathematics

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10.24033/bsmf.2774

Cite this

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title = "Nondegeneracy of nonradial sign-changing solutions to the nonlinear Schr{\"o}dinger equation",

abstract = "We prove that the non-radial sign-changing solutions to the nonlinear Schr{\"o}dinger equation ∆u − u + |u|p−1u = 0 in RN, u ∈ H1 (RN) constructed by Musso, Pacard, and Wei [16] are non-degenerate. This provides the first example of a non-degenerate sign-changing solution to the above nonlinear Schr{\"o}dinger equation with finite energy.",

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N2 - We prove that the non-radial sign-changing solutions to the nonlinear Schrödinger equation ∆u − u + |u|p−1u = 0 in RN, u ∈ H1 (RN) constructed by Musso, Pacard, and Wei [16] are non-degenerate. This provides the first example of a non-degenerate sign-changing solution to the above nonlinear Schrödinger equation with finite energy.

AB - We prove that the non-radial sign-changing solutions to the nonlinear Schrödinger equation ∆u − u + |u|p−1u = 0 in RN, u ∈ H1 (RN) constructed by Musso, Pacard, and Wei [16] are non-degenerate. This provides the first example of a non-degenerate sign-changing solution to the above nonlinear Schrödinger equation with finite energy.

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Nondegeneracy of nonradial sign-changing solutions to the nonlinear Schrödinger equation

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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