Mei Yu, Meina Zhang, Xia Zhang
In the framework of fractional Sobolev space, using Nehari manifold and concentration compactness principle, we study a minimization problem in the whole space involving the fractional Laplacian. Firstly, we give a Lions type lemma in fractional Sobolev space, which is crucial in the proof of our main result. Then, by showing a relative compactness of minimizing sequence, we obtain the existence of minimizer for the above-mentioned fractional minimization problem. Furthermore, we also point out that the minimizer is actually a ground state solution for the associated fractional Schrodinger equation
Submitted September 23, 2017. Published March 26, 2018.
Math Subject Classifications: 35A15, 35J60, 46E35.
Key Words: Minimization problem; fractional Schrodinger equation; ground state; Nehari manifold; concentration compactness principle.
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| Mei Yu |
Department of Applied Mathematics
Northwestern Polytechnical University
Xi'an, Shannxi, 710129, China
| Meina Zhang |
College of Science
Harbin Engineering University
Harbin 150001, China
| Xia Zhang |
Department of Mathematics
Harbin Institute of Technology, China
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