@article{Li2024, 
author = {Qi Li and Yuzhu Han and Bin Guo},
title = {A critical Kirchhoff problem with a logarithmic type perturbation in high dimension},
year = {2024},
journal = {Communications in Analysis and Mechanics},
volume = {16},
number = {3},
pages = {578-598},
keywords = {critical, Kirchhoff equation, logarithmic perturbation, high dimension, mountain pass lemma},
url = {https://www.sciopen.com/article/10.3934/cam.2024027},
doi = {10.3934/cam.2024027},
abstract = {In this paper, the following critical Kirchhoff-type elliptic equation involving a logarithmic-type perturbation   −(a+b∫Ω|∇u|2dx)Δu=λ|u|q−2uln⁡|u|2+μ|u|2uis considered in a bounded domain in  R4. One of the main obstructions one encounters when looking for weak solutions to Kirchhoff problems in high dimensions is that the boundedness of the  (PS) sequence is hard to obtain. By combining a result by Jeanjean [27] with the mountain pass lemma and Brézis–Lieb's lemma, it is proved that either the norm of the sequence of approximation solutions goes to infinity or the problem admits a nontrivial weak solution, under some appropriate assumptions on  a,  b,  λ, and  μ.}
}