Fractional minimization problem on the Nehari manifold

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dc.contributor.authorYu, Mei
dc.contributor.authorZhang, Meina
dc.contributor.authorZhang, Xia
dc.date.accessioned2022-01-31T16:33:09Z
dc.date.available2022-01-31T16:33:09Z
dc.date.issued2018-03-26
dc.description.abstractIn 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.departmentMathematics
dc.formatText
dc.format.extent21 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationYu, 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.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/15249
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.holderThis work is licensed under a Creative Commons Attribution 4.0 International License.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectMinimization problem
dc.subjectFractional Schrödinger equation
dc.subjectGround state
dc.subjectNehari manifold
dc.subjectConcentration compactness principle
dc.titleFractional minimization problem on the Nehari manifold
dc.typeArticle

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