Multiplicity of positive solutions for the fractional Schrödinger-Poisson system with critical nonlocal term
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Date
2024-08-28
Authors
Dou, Xilin
He, Xiaoming
Radulescu, Vicentiu
ORCID
0000-0003-4615-5537Advisor
Referee
Mark
Journal Title
Journal ISSN
Volume Title
Publisher
World Scientific
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Abstract
This paper deals with the following fractional Schrodinger-Poisson system: (-& UDelta;)su + u - K(x)f|u|2s*-3u = f ?(x)|u|q-2u,x & ISIN; Double-struck capital R3,(-& UDelta;)sf = K(x)|u|2s*-1,x & ISIN; Double-struck capital R3 with multiple competing potentials and a critical nonlocal term, where s & ISIN; (0, 1), q & ISIN; (1, 2) or q & ISIN; (4, 2s*), and 2s* = 6 3-2s is the fractional critical exponent. By combining the Nehari manifold analysis and the Ljusternik-Schnirelmann category theory, we establish how the coefficient K of the nonlocal critical nonlinearity affects the number of positive solutions. We propose a new relation between the number of positive solutions and the category of the global maximal set of K.
Description
Citation
Bulletin of Mathematical Sciences. 2024, vol. 14, issue 02, p. 1-56.
https://www.worldscientific.com/doi/epdf/10.1142/S1664360723500121
https://www.worldscientific.com/doi/epdf/10.1142/S1664360723500121
Document type
Peer-reviewed
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Published version
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Language of document
en