## Abstract

We construct sequences of sign-changing solutions for some conformally invariant semilinear elliptic equation which is defined S^{n}, when n ≥ 4. The solutions we obtain have large energy and concentrate along some special submanifolds of S^{n}. For example, for n ≥ 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} × {0} ⊂ S^{n}). In dimension n ≥ 5 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}).

Original language | English |
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Pages (from-to) | 209-237 |

Number of pages | 29 |

Journal | Annali della Scuola Normale - Classe di Scienze |

Volume | 12 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2013 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Mathematics (miscellaneous)