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On the fractional Lane-Emden equation. (English) Zbl 1515.35311

Summary: We classify solutions of finite Morse index of the fractional Lane-Emden equation \[ (-\Delta )^{s} u = | u|^{p-1}u \quad \text{in } \mathbb{R}^{n}. \]

MSC:

35R11 Fractional partial differential equations
35B65 Smoothness and regularity of solutions to PDEs
35J25 Boundary value problems for second-order elliptic equations
35S10 Initial value problems for PDEs with pseudodifferential operators
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