On general Kirchhoff type equations with steep potential well and critical growth in $ \mathbb{R}^2 $

On general Kirchhoff type equations with steep potential well and critical growth in $ \mathbb{R}^2 $

In this paper, we study the following Kirchhoff-type equation:$ \begin{equation*} M\left(\displaystyle{\int}_{\mathbb{R}^2}(|\nabla u|^2 +u^2)\mathrm{d} x\right)(-\Delta u+u) + \mu V(x)u = K(x) f(u) \ \ \mathrm{in} \ \ \mathbb{R}^2, \end{equation*} $where $ M \in C(\mathbb{R}^+, \mathbb{R}^+) $ is...

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Bibliographic Details
Main Authors: Zhenluo Lou, Jian Zhang
Format: Article
Language:English
Published: AIMS Press 2024-07-01
Series:AIMS Mathematics
Subjects:
kirchhoff-type equation
steep potential well
critical growth
dimension two
variational method
Online Access:https://www.aimspress.com/article/doi/10.3934/math.20241041?viewType=HTML

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https://www.aimspress.com/article/doi/10.3934/math.20241041?viewType=HTML

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