Existence results for Kirchhoff equations with Hardy–Littlewood–Sobolev critical nonlinearity

Existence results for Kirchhoff equations with Hardy–Littlewood–Sobolev critical nonlinearity

In this paper, we study a class of Kirchhoff equations with Hardy–Littlewood–Sobolev critical nonlinearity in RN. More precisely, we consider −a+b∫RN|∇u|2dxΔu−a[Δ(u2)]u=λIμ∗|u|p|u|p−2u+Iμ∗|u|22μ∗|u|22μ∗−2u, where a>0, b≥0, N≥3, 0

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Veröffentlicht in:Nonlinear analysis 2020-09, Vol.198, p.111900, Article 111900
Hauptverfasser: Song, Yueqiang, Zhao, Fu, Pu, Hongling, Shi, Shaoyun
Format: Artikel
Sprache:eng
Schlagworte:
Concentration–compactness principle
Hardy–Littlewood–Sobolev critical exponent
Kirchhoff problem
Mathematical analysis
Nonlinearity
Variational methods
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Zusammenfassung:In this paper, we study a class of Kirchhoff equations with Hardy–Littlewood–Sobolev critical nonlinearity in RN. More precisely, we consider −a+b∫RN|∇u|2dxΔu−a[Δ(u2)]u=λIμ∗|u|p|u|p−2u+Iμ∗|u|22μ∗|u|22μ∗−2u, where a>0, b≥0, N≥3, 0
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2020.111900