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

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].

To appear in American Journal of Math. 19 pages

References in corpus (2)

• On higher order extensions for the fractional Laplacian
• A Liouville Theorem for the Fractional Laplacian