Existence and Asymptotic Behavior of Localized Nodal Solutions for a Class of Kirchhoff-Type Equations
Existence and Asymptotic Behavior of Localized Nodal Solutions for a Class of Kirchhoff-Type Equations
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一类基尔霍夫方程组局部节点解的存在性及其渐近行为
DOI：
10.1007/s12220-021-00722-0
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Jian Zhang
中科院分区：
文献类型：
--
作者：
Quanqing Li;Jianjun Nie;Wenbo Wang;Jian Zhang
In this paper, we study the existence and asymptotic behavior of localized nodal solutions for the following Kirchhoff-type equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} -\left( \varepsilon ^2a+\varepsilon b\int _{\mathbb {R}^3}|\nabla u|^2dx\right) \Delta u+V(x)u=|u|^{p-2}u, \ x \in \mathbb {R}^3, \end{aligned}$$\end{document}where,and. Under only a local condition thatVhas a local trapping potential well, whenis sufficiently small, we construct the existence of a sequence of localized nodal solutions concentrating around the local minimum points of the potential functionVby using variational method and penalization approach. Moreover, we regardbas a parameter and study the asymptotic behavior of the nodal solutions as, which reflects some relationship betweenand.
In this paper, we study the existence and asymptotic behavior of localized nodal solutions for the following Kirchhoff-type equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} -\left( \varepsilon ^2a+\varepsilon b\int _{\mathbb {R}^3}|\nabla u|^2dx\right) \Delta u+V(x)u=|u|^{p-2}u, \ x \in \mathbb {R}^3, \end{aligned}$$\end{document}where,and. Under only a local condition thatVhas a local trapping potential well, whenis sufficiently small, we construct the existence of a sequence of localized nodal solutions concentrating around the local minimum points of the potential functionVby using variational method and penalization approach. Moreover, we regardbas a parameter and study the asymptotic behavior of the nodal solutions as, which reflects some relationship betweenand.