期刊
NONLINEARITY
卷 28, 期 6, 页码 1937-1961出版社
IOP PUBLISHING LTD
DOI: 10.1088/0951-7715/28/6/1937
关键词
fractional Laplacian; ground states; concentration phenomena; uniqueness
资金
- Alexander von Humboldt Foundation
- International Center for Theoretical Physics ( ICTP)
- Fondecyt [1140311]
- Millennium Nucleus Center for Analysis of PDE [NC130017]
- ERC
- PRIN
We consider here solutions of the nonlinear fractional Schrodinger equation epsilon(2s) (-Delta)(s) u + V (x) u = u(p). We show that concentration points must be critical points for V. We also prove that if the potential V is coercive and has a unique global minimum, then ground states concentrate suitably at such a minimal point as epsilon tends to zero. In addition, if the potential V is radial and radially decreasing, then the minimizer is unique provided epsilon is small.
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