Non-radial singular solutions of Lane-Emden equations in $R^N$ E. DancerZhenhua GuoJuncheng Wei 35J25Nonradial Singular SolutionsSupercritical Lane-Emden EquationsAsymptotic Analysis We obtain infinitely many non-radial singular solutions of the Lane-Emden equation \[ \Delta u+u^p=0\quad\mbox{in }\mathbb{R}^N\setminus\{0\},\ N\geq4\] with\[\frac{N+1}{N-3}<p<p_c(N-1)\] by constructing infinitely many radially symmetric regular solutions of equation on $S^{N-1}$:\[\Delta_{S^{N-1}}w-\frac{2}{p-1}\left[N-2-\frac{2}{p-1}\right]w+w^p=0.\] Indiana University Mathematics Journal 2012 text pdf 10.1512/iumj.2012.61.4749 10.1512/iumj.2012.61.4749 en Indiana Univ. Math. J. 61 (2012) 1971 - 1996 state-of-the-art mathematics http://iumj.org/access/