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

Keywords

Orthogonality condition
Schrödinger equation
Sign-changing solution

ASJC Scopus subject areas

Mathematics(all)

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10.24033/bsmf.2774

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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.",

keywords = "Orthogonality condition, Schr{\"o}dinger equation, Sign-changing solution",

author = "Weiwei Ao and Monica Musso and Juncheng Wei",

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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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KW - Schrödinger equation

KW - Sign-changing solution

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

Abstract

Keywords

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