Geodesic
Nondegeneracy of nonradial sign-changing solutions to the nonlinear Schrödinger equation
[Non dégéneration de solutions non radiales qui changent de signe à l’équation non linéaire de Schrödinger]
Ao, Weiwei1 ; Musso, Monica2, 3 ; Wei, Juncheng4
1 Department of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China
2 Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom
3 Departamento de Matemática, Pontificia Universidad Catolica de Chile, Avda. Vicuña Mackenna 4860, Macul, Chile
4 Department of Mathematics, University of British Columbia, Vancouver, BC V6T1Z2, Canada
Bulletin de la Société Mathématique de France, Tome 147 (2019) no. 1, pp. 1-48

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We prove that the non-radial sign-changing solutions to the nonlinear Schrödinger equation

Δ u - u + | u | p - 1 u = 0 in ℝ N , u ∈ H 1 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.

Nous prouvons que les solutions non radiales qui changent de signe à l’équation non linéaire de Schrödinger

Δ u - u + | u | p - 1 u = 0 in ℝ N , u ∈ H 1 ℝ N

qui ont été construits par Musso, Pacard, Wei [16] sont non dégénérées. Ceci fournit le premier exemple de solutions qui changent de signe à l’équation non linéaire de Schrödinger avec énergie finie.

DOI : 10.24033/bsmf.2774
Classification : 35B10, 92C40, 35B32
Keywords: Schrödinger equation, sign-changing solution, orthogonality condition
Mots-clés : Non-degeneracy, sign-changing solution, Schrodinger equation

Ao, Weiwei 1 ; Musso, Monica 2, 3 ; Wei, Juncheng 4

1 Department of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China
2 Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom
3 Departamento de Matemática, Pontificia Universidad Catolica de Chile, Avda. Vicuña Mackenna 4860, Macul, Chile
4 Department of Mathematics, University of British Columbia, Vancouver, BC V6T1Z2, Canada 
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     author = {Ao, Weiwei and Musso, Monica and Wei, Juncheng},
     title = {Nondegeneracy of nonradial sign-changing solutions to the nonlinear {Schr\"odinger} equation},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {1--48},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {147},
     number = {1},
     year = {2019},
     doi = {10.24033/bsmf.2774},
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     zbl = {1437.35379},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.24033/bsmf.2774/}
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Ao, Weiwei; Musso, Monica; Wei, Juncheng. Nondegeneracy of nonradial sign-changing solutions to the nonlinear Schrödinger equation. Bulletin de la Société Mathématique de France, Tome 147 (2019) no. 1, pp. 1-48. doi: 10.24033/bsmf.2774

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