Fractional minimization problem on the Nehari manifold
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Date
2018-03-26
Authors
Yu, Mei
Zhang, Meina
Zhang, Xia
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Minimization problem, Fractional Schrödinger equation, Ground state, Nehari manifold, Concentration compactness principle
Citation
Yu, M., Zhang, M., & Zhang, X. (2018). Fractional minimization problem on the Nehari manifold. <i>Electronic Journal of Differential Equations, 2018</i>(82), pp. 1-21.
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Attribution 4.0 International
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This work is licensed under a Creative Commons Attribution 4.0 International License.