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

Published online by Cambridge University Press:  11 July 2007

X. Xu
X. Xu
Affiliation:
Department of Mathematics, National University of Singapore, Lower Kent Ridge Road, Singapore 119260, Republic of Singapore (matxuxw@math.nus.edu.sg)
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Abstract

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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 130 , Issue 3 , June 2000 , pp. 651 - 670
Copyright
Copyright © Royal Society of Edinburgh 2000

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