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On finite Morse index solutions of higher order fractional Lane-Emden equations
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 139, Number 2, April 2017
- pp. 433-460
- 10.1353/ajm.2017.0011
- Article
- Additional Information
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We classify finite Morse index solutions of the following nonlocal Lane-Emden equation $$(-\Delta)^{s} u=|u|^{p-1} u\quad {\Bbb R}^n$$ for $1<s<2$ via a novel monotonicity formula. For local cases $s=1$ and $s=2$ this classification was provided by Farina in 2007 and D{\'a}vila, Dupaigne, Wang, and Wei in 2014, respectively. Moreover, for the nonlocal case $0<s<1$ finite Morse index solutions are classified by D{\'a}vila, Dupaigne, and Wei in their 2014 preprint.