Uniqueness of Radial Solutions for the Fractional Laplacian

• Published in: Communications on pure and applied mathematics Vol. 69; no. 9; pp. 1671 - 1726
• Main Authors: Frank, Rupert L., Lenzmann, Enno, Silvestre, Luis
• Format: Journal Article
• Language: English
• Published: New York Blackwell Publishing Ltd 01.09.2016; John Wiley and Sons, Limited
• Subjects: Laplace transforms; Linear equations; Nonlinear equations; Schrodinger equation

We prove general uniqueness results for radial solutions of linear and nonlinear equations involving the fractional Laplacian (−Δ)s with s ∊ (0,1) for any space dimensions N ≥ 1. By extending a monotonicity formula found by Cabré and Sire , we show that the linear equation (−Δ)su+Vu=0 in ℝN has at m...