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.

We construct sequences of sign-changing solutions for some conformally invariant semilinear elliptic equation which is defined S n , when n4. The solutions we obtain have large energy and concentrate along some special submanifolds of S n . For example, for n4 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 ×{0}S n ). In dimension n5 we obtain sequences of solutions whose energy concentrates along a two-dimensional torus (which corresponds to a Clifford torus embedded in S 3 ×{0}S n ).

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Classification: 53C21,  35J65
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     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},
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     year = {2013},
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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, 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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