Torus action on $S^{n}$ and sign-changing solutions for conformally invariant equations

del Pino, Manuel; Musso, Monica; Pacard, Frank; Pistoia, Angela

Torus action on

S^{n}

and sign-changing solutions for conformally invariant equations

del Pino, Manuel ; Musso, Monica ; Pacard, Frank ; Pistoia, Angela

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 12 (2013) no. 1, pp. 209-237.

Résumé

We construct sequences of sign-changing solutions for some conformally invariant semilinear elliptic equation which is defined $S^{n}$ , when $n \geq 4$ . The solutions we obtain have large energy and concentrate along some special submanifolds of $S^{n}$ . For example, for $n \geq 4$ 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 $S^{3} \times {0} \subset S^{n}$ ). In dimension $n \geq 5$ we obtain sequences of solutions whose energy concentrates along a two-dimensional torus (which corresponds to a Clifford torus embedded in $S^{3} \times {0} \subset S^{n}$ ).

Publié le : 2019-02-21

MR Zbl | 1 citation dans Numdam

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},
     pages = {209--237},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 12},
     number = {1},
     year = {2013},
     mrnumber = {3088442},
     zbl = {1267.53040},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2013_5_12_1_209_0/}
}

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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, Série 5, Tome 12 (2013) no. 1, pp. 209-237. http://www.numdam.org/item/ASNSP_2013_5_12_1_209_0/

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