含有对数非线性项Kirchhoff方程多解的存在性

数学物理学报 ›› 2022, Vol. 42 ›› Issue (2): 401-417.

含有对数非线性项Kirchhoff方程多解的存在性

胡蝶(),高琦*()

武汉理工大学理学院数学系武汉 430070

收稿日期:2021-08-02 出版日期:2022-04-26 发布日期:2022-04-18
通讯作者: 高琦 E-mail:hudie8062@163.com;gaoq@whut.edu.cn
作者简介:胡蝶，E-mail: hudie8062@163.com
基金资助:
国家自然科学基金(11871386);国家自然科学基金(11931012);中央高校基本科研业务费专项基金(WUT: 2020IB019)

Multiple Solutions to Logarithmic Kirchhoff Equations

Die Hu(),Qi Gao*()

Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan 430070

Received:2021-08-02 Online:2022-04-26 Published:2022-04-18
Contact: Qi Gao E-mail:hudie8062@163.com;gaoq@whut.edu.cn
Supported by:
the NSFC(11871386);the NSFC(11931012);the Fundamental Research Funds for the Central Universities(WUT: 2020IB019)

摘要/Abstract

摘要：

该文考虑如下带有对数非线性项的Kirchhoff方程 $\begin{eqnarray*} -\Big(a+b\int_{\mathbb{R} ^{3}}\left | \nabla u \right |^{2}{\rm d}x\Big)\Delta u+V(x)u=|u|^{p-2}u{\rm log}u^{2}, \ \ \ \ x\in \mathbb{R} ^3, \end{eqnarray*}$ 其中$p\in(4, 6)$, $a, b>0$为常数, 位势函数$V(x)\in {\cal C}(\mathbb{R} ^{3}, \mathbb{R})$.运用约束变分法, 形变引理和度理论, 该文证明了上述问题在不同的位势条件下存在正解和变号解.

关键词: 对数Kirchhoff方程, 变号解, 正解

Abstract:

We study a class of logarithmic Kirchhoff equations with two types of potentials, and obtain the existence of positive solutions and sign-changing solutions.

Key words: Logarithmic Kirchhoff equations, Sign-changing solution, Positive solutions

中图分类号:

O175.2

胡蝶,高琦. 含有对数非线性项Kirchhoff方程多解的存在性[J]. 数学物理学报, 2022, 42(2): 401-417.

Die Hu,Qi Gao. Multiple Solutions to Logarithmic Kirchhoff Equations[J]. Acta mathematica scientia,Series A, 2022, 42(2): 401-417.

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