Abstract
In this paper, we consider the following Yamabe type problem of polyharmonic operator:(P){Dmu=|u|4mN−2muon SN,u∈Hm(SN), where N⩾2m+1, m∈N+, SN, is the unit sphere with the induced Riemannian metric g=gSN, and Dm is the elliptic differential operator of 2m order given byDm=∏k=1m(−Δg+14(N−2k)(N+2k−2)), where Δg is the Laplace–Beltrami operator on SN. We will show that the problem (P) has infinitely many non-radial sign-changing solutions.
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