Torus action on <i>S<SUP>n</SUP></i> and sign-changing solutions for conformally invariant equations
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Date
2013
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Abstract
We construct sequences of sign-changing solutions for some conformany 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 x {0) subset of 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 x {0} subset of S-n).