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
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10.1512/iumj.2012.61.4749
10.1512/iumj.2012.61.4749
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Indiana Univ. Math. J. 61 (2012) 1971 - 1996
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