Torus action on S^n and sign changing solutions for conformally invariant equations

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 ).