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non-removable singularity of $u(x)$}. \\end{equation} It is known from [Theorem 4.2] that any positive entire solution $u$ of \\eqref{0.0} is radially symmetric with respect to $x=0$, i.e. $u(x)=u(|x|)$, and equation \\eqref{0.0} also admits a special positive entire solution $u_s (x)=\\Big(\\frac{n^2 (n-4)^2}{16} \\Big)^{\\frac{n-4}{8}} 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Delaunay solutions of a biharmonic elliptic equation with critical exponent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Liping Wang, Xia Huang, Zongming Guo","submitted_at":"2017-08-15T19:52:11Z","abstract_excerpt":"We are interested in the qualitative properties of positive entire solutions $u \\in C^4 (\\mathbb{R}^n \\backslash \\{0\\})$ of the equation \\begin{equation} \\label{0.0} \\Delta^2 u=u^{\\frac{n+4}{n-4}} \\;\\;\\mbox{in $\\mathbb{R}^n \\backslash \\{0\\}$ and 0 is a non-removable singularity of $u(x)$}. \\end{equation} It is known from [Theorem 4.2] that any positive entire solution $u$ of \\eqref{0.0} is radially symmetric with respect to $x=0$, i.e. $u(x)=u(|x|)$, and equation \\eqref{0.0} also admits a special positive entire solution $u_s (x)=\\Big(\\frac{n^2 (n-4)^2}{16} \\Big)^{\\frac{n-4}{8}} 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