Multiple solutions for critical Choquard-Kirchhoff type equations

In this article, we investigate multiplicity results for Choquard-Kirchhoff type equations, with Hardy-Littlewood-Sobolev critical exponents, where > 0, ≥ 0, 0 < < , ≥ 3, and are positive real parameters, is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality, ∈ (ℝ ),...

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Bibliographic Details
Published inAdvances in nonlinear analysis Vol. 10; no. 1; pp. 400 - 419
Main Authors Liang, Sihua, Pucci, Patrizia, Zhang, Binlin
Format Journal Article
LanguageEnglish
Published De Gruyter 01.01.2021
Subjects
35A15
35B33
35J20
35J60
Choquard nonlinearity
Concentraction compactness principle
Hardy-Littlewood-Sobolev critical exponent
Kirchhoff equation
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Summary:In this article, we investigate multiplicity results for Choquard-Kirchhoff type equations, with Hardy-Littlewood-Sobolev critical exponents, where > 0, ≥ 0, 0 < < , ≥ 3, and are positive real parameters, is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality, ∈ (ℝ ), with = 2 /(2 − ) if 1 < < 2 and = ∞ if ≥ 2 . According to the different range of , we discuss the multiplicity of solutions to the above equation, using variational methods under suitable conditions. In order to overcome the lack of compactness, we appeal to the concentration compactness principle in the Choquard-type setting.
ISSN:2191-9496
2191-950X
DOI:10.1515/anona-2020-0119