article

Title: Non-radial singular solutions of Lane-Emden equations in $R^N$

Authors: E.N. Dancer, Zongming Guo and Juncheng Wei

Issue: Volume 61 (2012), Issue 5, 1971-1996

Abstract:

$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 $S^{N-1}$:\[\Delta_{S^{N-1}}w-\frac{2}{p-1}\left[N-2-\frac{2}{p-1}\right]w+w^p=0.\]$