Torus action on ${S}^{n}$ and sign-changing solutions for conformally invariant equations
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 12 (2013) no. 1, p. 209-237

We construct sequences of sign-changing solutions for some conformally invariant semilinear elliptic equation which is defined ${S}^{n}$, when $n\ge 4$. The solutions we obtain have large energy and concentrate along some special submanifolds of ${S}^{n}$. For example, for $n\ge 4$ we obtain sequences of solutions whose energy concentrates along one great circle or finitely many great circles which are linked to each other (and they correspond to Hopf links embedded in ${S}^{3}×\left\{0\right\}\subset {S}^{n}$). In dimension $n\ge 5$ we obtain sequences of solutions whose energy concentrates along a two-dimensional torus (which corresponds to a Clifford torus embedded in ${S}^{3}×\left\{0\right\}\subset {S}^{n}$).

Published online : 2019-02-21
Classification:  53C21,  35J65
@article{ASNSP_2013_5_12_1_209_0,
author = {del Pino, Manuel and Musso, Monica and Pacard, Frank and Pistoia, Angela},
title = {Torus action on $S^{n}$ and sign-changing solutions for conformally invariant equations},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 12},
number = {1},
year = {2013},
pages = {209-237},
zbl = {1267.53040},
mrnumber = {3088442},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2013_5_12_1_209_0}
}

del Pino, Manuel; Musso, Monica; Pacard, Frank; Pistoia, Angela. Torus action on $S^{n}$ and sign-changing solutions for conformally invariant equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 12 (2013) no. 1, pp. 209-237. http://www.numdam.org/item/ASNSP_2013_5_12_1_209_0/

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