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

2014/10/20 by Mostafa Fazly, Juncheng Wei, Fazly, Mostafa +1 · 2 citations
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1410.5400

To appear in American Journal of Math. 19 pages

arxiv created 2015/10/30 · arxiv updated 2015/11/03

Abstract

We classify finite Morse index solutions of the fractional Lane-Emden equation (-Δ)^s u=|u|^p-1 u ℝⁿ 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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• Multiple solutions for elliptic equations driven by higher order fractional Laplacian
• On stable solutions of the fractional Henon-Lane-Emden equation

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