Large energy entire solutions for the Yamabe type problem of polyharmonic operator

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