期刊
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
卷 69, 期 9, 页码 1671-1726出版社
WILEY
DOI: 10.1002/cpa.21591
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资金
- National Science Foundation [PHY-1068285, PHY-1347399, DMS-1363432, DMS-1001629, DMS-1065979]
- Swiss National Science Foundation (SNF)
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1254332] Funding Source: National Science Foundation
We prove general uniqueness results for radial solutions of linear and nonlinear equations involving the fractional Laplacian (-)(s) with s(0,1) for any space dimensions N1. By extending a monotonicity formula found by Cabre and Sire , we show that the linear equation has at most one radial and bounded solution vanishing at infinity, provided that the potential V is radial and nondecreasing. In particular, this result implies that all radial eigenvalues of the corresponding fractional Schrodinger operator H = (-)(s)+V are simple. Furthermore, by combining these findings on linear equations with topological bounds for a related problem on the upper half-space +N+1, we show uniqueness and nondegeneracy of ground state solutions for the nonlinear equation for arbitrary space dimensions N1 and all admissible exponents >0. This generalizes the nondegeneracy and uniqueness result for dimension N = 1 recently obtained by the first two authors and, in particular, the uniqueness result for solitary waves of the Benjamin-Ono equation found by Amick and Toland .(c) 2016 Wiley Periodicals, Inc.
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