Yu, MeiZhang, MeinaZhang, Xia2022-01-312022-01-312018-03-26Yu, M., Zhang, M., & Zhang, X. (2018). Fractional minimization problem on the Nehari manifold. <i>Electronic Journal of Differential Equations, 2018</i>(82), pp. 1-21.1072-6691https://hdl.handle.net/10877/15249In 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.Text21 pages1 file (.pdf)enAttribution 4.0 InternationalMinimization problemFractional Schrödinger equationGround stateNehari manifoldConcentration compactness principleArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.