Abstract.
In this paper, we consider the following conformally invariant equations of fourth order¶\( \cases {\Delta^2 u = 6 e^{4u} &in $\bf {R}^4,$ \cr e^{4u} \in L^1(\bf {R}^4),\cr}\)(1)¶and¶\( \cases {\Delta^2 u = u^{n+4 \over n-4}, \cr u>0 & in $ {\bf R}^n $ \qquad for $ n \ge5 $, \cr} \)(2) where \( \Delta^2 \) denotes the biharmonic operator in R n. By employing the method of moving planes, we are able to prove that all positive solutions of (2) are arised from the smooth conformal metrics on S n by the stereograph projection. For equation (1), we prove a necessary and sufficient condition for solutions obtained from the smooth conformal metrics on S 4.
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Received: September 26, 1996
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Lin, CS. A classification of solutions of a conformally invariant fourth order equation in Rn. Comment. Math. Helv. 73, 206–231 (1998). https://doi.org/10.1007/s000140050052
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DOI: https://doi.org/10.1007/s000140050052