Fractional minimization problem on the Nehari manifold
dc.contributor.author | Yu, Mei | |
dc.contributor.author | Zhang, Meina | |
dc.contributor.author | Zhang, Xia | |
dc.date.accessioned | 2022-01-31T16:33:09Z | |
dc.date.available | 2022-01-31T16:33:09Z | |
dc.date.issued | 2018-03-26 | |
dc.description.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. | |
dc.description.department | Mathematics | |
dc.format | Text | |
dc.format.extent | 21 pages | |
dc.format.medium | 1 file (.pdf) | |
dc.identifier.citation | Yu, M., Zhang, M., & Zhang, X. (2018). Fractional minimization problem on the Nehari manifold. Electronic Journal of Differential Equations, 2018(82), pp. 1-21. | |
dc.identifier.issn | 1072-6691 | |
dc.identifier.uri | https://hdl.handle.net/10877/15249 | |
dc.language.iso | en | |
dc.publisher | Texas State University, Department of Mathematics | |
dc.rights | Attribution 4.0 International | |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
dc.source | Electronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas. | |
dc.subject | Minimization problem | |
dc.subject | Fractional Schrödinger equation | |
dc.subject | Ground state | |
dc.subject | Nehari manifold | |
dc.subject | Concentration compactness principle | |
dc.title | Fractional minimization problem on the Nehari manifold | |
dc.type | Article |