On Kirchhoff type equations with critical Sobolev exponent

We study the following Brezis–Nirenberg problem of Kirchhoff type{−(a+b∫Ω|∇u|2dx)Δu=λ|u|q−2u+δ|u|2u,inΩ,u=0,on∂Ω, where Ω⊂R4 is a bounded domain with the smooth boundary ∂Ω, 2≤q

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2018-06, Vol.462 (1), p.483-504
Main Authors: Huang, Yisheng, Liu, Zeng, Wu, Yuanze
Format: Article
Language:English
Subjects:
Critical
Kirchhoff type equation
Nonlocal problem
Perturbation method
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Summary:We study the following Brezis–Nirenberg problem of Kirchhoff type{−(a+b∫Ω|∇u|2dx)Δu=λ|u|q−2u+δ|u|2u,inΩ,u=0,on∂Ω, where Ω⊂R4 is a bounded domain with the smooth boundary ∂Ω, 2≤q
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2018.02.023