对数
非线性系统
兰姆达
类型(生物学)
数学
组合数学
数学分析
能量(信号处理)
内哈里歧管
数学物理
国家(计算机科学)
符号(数学)
物理
量子力学
生态学
算法
生物
作者
Ling Huang,L. Wang,Hui Feng
出处
期刊:Authorea - Authorea
日期:2024-01-31
标识
DOI:10.22541/au.170667346.62313991/v1
摘要
\begin{abstract} {In this paper, we study a class of critical fractional Kirchhoff-type equations involving logarithmic nonlinearity and steep potential well in $\R^N$ as following: \begin{align*} \renewcommand{\arraystretch}{1.25} \begin{array}{ll} \ds \left \{ \begin{array}{ll} \ds \left(a+b\int_{\R^{N}}|(-\Delta)^\frac{s}{2}u|^2\, dx\right)(-\Delta)^s u+\mu V(x)u=\lambda a(x)u\ln|u|+|u|^{2_{s}^{*}-2}u~~~\text{in}~\mathbb{R}^N, \\ u\in H^s(\R^N), \\ \end{array} \right . \end{array} \end{align*} where $a>0$ is a constant, $b$ is a positive parameter, $s\in(0,1)$ and $N>4s,$ $\mu>0$ is a parameter and $V(x)$ satisfies some assumptions that will be specified later. By applying the Nehari manifold method, we obtain that such equation with sign-changing weight potentials admits at least one positive ground state solution and the associated energy is negative. Moreover, we also explore the asymptotic behavior as $b\to 0$ and $\mu\to\infty,$ respectively.}
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