@article{Lou2024, 
author = {Zhenluo Lou and Jian Zhang},
title = {On general Kirchhoff type equations with steep potential well and critical growth in  R2},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {8},
pages = {21433-21454},
keywords = {Kirchhoff-type equation, steep potential well, critical growth, dimension two, variational method},
url = {https://www.sciopen.com/article/10.3934/math.20241041},
doi = {10.3934/math.20241041},
abstract = {In this paper, we study the following Kirchhoff-type equation:   M(∫R2(|∇u|2+u2)dx)(−Δu+u)+μV(x)u=K(x)f(u)inR2,where  M∈C(R+,R+) is a general function,  V≥0 and its zero set may have several disjoint connected components,  μ>0 is a parameter,  K is permitted to be unbounded above, and  f has exponential critical growth. By using the truncation technique and developing some approaches to deal with Kirchhoff-type equations with critical growth in the whole space, we get the existence and concentration behavior of solutions. The results are new even for the case  M≡1.}
}