Uniqueness theorem for the entire positive solutions of biharmonic equations in Rn

X. Xu

doi:10.1017/S0308210500000354

Abstract

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The entire positive solutions of a conformally invariant biharmonic equation in Rn will be classified using the method of moving spheres. As a byproduct, one also shows that any entire non-negative solution of the equation Δ2u = up with 1 ≤ p < (n + 4)/(n−4) with n ≥ 2 is zero.

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Uniqueness theorem for the entire positive solutions of biharmonic equations in Rn

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