On the fractional Lane-Emden equation

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We classify solutions of finite Morse index of the fractional Lane-Emden equation (−∆) s u = |u| p−1 u in R n .

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On fractional elliptic equations in Lipschitz sets and epigraphs: regularity, monotonicity and rigidity results (2016, background): “onicity and rigidity of solutions to semilinear elliptic equations of fractional order in the whole space RN or in smooth bounded sets has attracted considerable attention in the last years, see e.g. [3,8,9,10,11,15,19,20,28,29,43]. In striking contrast, if is unbounded, but dierent from the whole s”
On finite Morse index solutions of higher order fractional Lane-Emden equations (2014, methodology): “stimates for solutions of (1.1). These estimates are needed in the next section when we perform a blow-down analysis argument. The methods and ideas provided in this section are strongly motivated by [7, 8]. Lemma 4.1. The following identities hold for any functions ζand η, ∆bζ∆b(ζη 2) −|∆ (4.1) b(ζ”