Hénon型椭圆系统多个非径向对称解的存在性

数学物理学报 ›› 2021, Vol. 41 ›› Issue (3): 723-728.

Hénon型椭圆系统多个非径向对称解的存在性

贾小尧(),娄振洛*()

^{河南科技大学数学与统计学院河南洛阳 471023}

收稿日期:2020-05-19 出版日期:2021-06-26 发布日期:2021-06-09
通讯作者: 娄振洛 E-mail:jiaxiaoyao@haust.edu.cn;louzhenluo@amss.ac.cn
作者简介:贾小尧, E-mail: jiaxiaoyao@haust.edu.cn
基金资助:
国家自然科学基金(11571339);国家自然科学基金(11871195);国家自然科学基金(11301153);河南科技大学博士启动基金(13480051);河南省高等学校重点科研项目(20B110004)

Existence of Multiple Non-Radial Positive Solutions of a Hénon Type Elliptic System

Xiaoyao Jia(),Zhenluo Lou*()

^{Mathematics and Statistics School, Henan University of Science and Technology, Henan Luoyang 471023}

Received:2020-05-19 Online:2021-06-26 Published:2021-06-09
Contact: Zhenluo Lou E-mail:jiaxiaoyao@haust.edu.cn;louzhenluo@amss.ac.cn
Supported by:
NSFC(11571339);NSFC(11871195);NSFC(11301153);the Doctoral Researcher Fundation of Henan University of Science and Technology(13480051);the Key Scientific Research Projects of Higher Education Institutions in Henan Province(20B110004)

摘要/Abstract

摘要：

该文研究如下椭圆系统 $\begin{eqnarray*}\left\{\begin{array}{ll}-\Delta u+\mu_1 u=\frac{p}{p+q}|x|^\alpha u^{p-1}v^q，~~&x\in\Omega，\[3mm]-\Delta v+\mu_2 v=\frac{q}{p+q}|x|^\alpha u^pv^{q-1}，~~&x\in\Omega，\[2mm]u，v>0，~~x\in\Omega，~~u=v=0，~&x\in~\partial\Omega，\end{array}\right.\end{eqnarray*}$ 此处 $\Omega\subset\mathbb{R}^N$ （ $N\geq4$ ）是一个圆环， $\mu_1，\mu_2>0$ ， $p，q>0$ 且 $p+q<\frac{2N-2}{N-3}$ .该文利用变分法和伸缩技巧证明上述系统有多个非径向对称解.

关键词: 椭圆系统, 变分法, 非径向对称解

Abstract:

In this paper, we study the following elliptic system $\begin{eqnarray*} \left\{\begin{array}{ll} -\Delta u+\mu_1 u=\frac{p}{p+q}|x|^\alpha u^{p-1}v^q, \ &x\in\Omega, \[3mm] -\Delta v+\mu_2 v=\frac{q}{p+q}|x|^\alpha u^pv^{q-1}, \ &x\in\Omega, \[2mm] u, v>0, ~x\in\Omega, ~~u=v=0, ~~&x\in\partial\Omega, \end{array}\right. \end{eqnarray*}$ where $\Omega\subset\mathbb{R}^N$ is an annulus $N\geq 4$ , $\mu_1, \mu_2>0$ , $p, q>1$ and $p+q<\frac{2N-2}{N-3}$ . By variational method and rescaling method, we prove that the system has many non-radial solutions.

Key words: Elliptic system, Variational method, Non-radial solutions

中图分类号:

O175.25

贾小尧,娄振洛. Hénon型椭圆系统多个非径向对称解的存在性[J]. 数学物理学报, 2021, 41(3): 723-728.

Xiaoyao Jia,Zhenluo Lou. Existence of Multiple Non-Radial Positive Solutions of a Hénon Type Elliptic System[J]. Acta mathematica scientia,Series A, 2021, 41(3): 723-728.

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