Mei Yu, Meina Zhang, Xia Zhang
Abstract:
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.
Show me the PDF file (279 KB), TEX file for this article.
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Mei Yu Department of Applied Mathematics Northwestern Polytechnical University Xi'an, Shannxi, 710129, China email: yumei@nwpu.edu.cn |
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Meina Zhang College of Science Harbin Engineering University Harbin 150001, China email: meina_zhang1@163.com |
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Xia Zhang Department of Mathematics Harbin Institute of Technology, China email: zhangxia@hit.edu.cn |
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