Large energy entire solutions for the Yamabe type problem of polyharmonic operator
نویسندگان
چکیده
In this paper, we consider the following Yamabe type problem of polyharmonic operator : { Dmu = |u| 4m N−2m u on S u ∈ H(S ), (P ) where N ≥ 2m + 1,m ∈ N+, S is the unit sphere with the induced Riemannian metric g = gSN , and Dm is the elliptic differential operator of 2m order given by Dm = m ∏ k=1 (−∆g + 14(N − 2k)(N + 2k − 2)) where ∆g is the Laplace-Beltrami operator on S . We will show that the problem (P) has infinitely many non-radial sign changing solutions.
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