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Bound states of fractional Choquard equations with Hardy-Littlewood-Sobolev critical exponent.
- Source :
-
Journal of Differential Equations . May2023, Vol. 355, p219-247. 29p. - Publication Year :
- 2023
-
Abstract
- We deal with the following fractional Choquard equation (− Δ) s u + V (x) u = (I μ ⁎ | u | 2 μ , s ⁎ ) | u | 2 μ , s ⁎ − 2 u , x ∈ R N , where I μ (x) is the Riesz potential, s ∈ (0 , 1) , 2 s < N ≠ 4 s , 0 < μ < min { N , 4 s } and 2 μ , s ⁎ = 2 N − μ N − 2 s is the fractional critical Hardy-Littlewood-Sobolev exponent. By combining variational methods and the Brouwer degree theory, we investigate the existence and multiplicity of positive bound solutions to this equation when V (x) is a positive potential bounded from below. The results obtained in this paper extend and improve some recent works in the case where the coefficient V (x) vanishes at infinity. [ABSTRACT FROM AUTHOR]
- Subjects :
- *BOUND states
*TOPOLOGICAL degree
*EQUATIONS
*DIFFERENTIAL equations
Subjects
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 355
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 162475080
- Full Text :
- https://doi.org/10.1016/j.jde.2023.01.023