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arXiv · 1410.5400

On finite Morse index solutions of higher order fractional Lane-Emden equations

Mostafa Fazly·Juncheng Wei
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Abstract

We classify finite Morse index solutions of the fractional Lane-Emden equation $(-\Delta)^{s} u=|u|^{p-1} u \ \ \ \mathbb{R}^n $ for $1<s<2$. For the local case, $s=1$ and $s=2$ this classification was done by Farina in [10] and Davila, Dupaigne, Wang and Wei in [8], respectively. Moreover, for the nonlocal case, $0<s<1$, finite Morse index solutions are classified by Davila, Dupaigne and Wei in [7].

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Mostafa Fazly, Juncheng Wei. 2014-10-20. On finite Morse index solutions of higher order fractional Lane-Emden equations. https://arxiv.org/abs/1410.5400

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