拟线性椭圆系统非径向爆破解的非存在性

数学物理学报 ›› 2019, Vol. 39 ›› Issue (2): 307-315.

拟线性椭圆系统非径向爆破解的非存在性

计婷¹,胡良根^1,*(),曾晶²

¹ 宁波大学数学系浙江宁波 315211
² 福建师范大学数学与计算机学院福州 350007

收稿日期:2017-10-12 出版日期:2019-04-26 发布日期:2019-05-05
通讯作者: 胡良根 E-mail:hulianggen@tom.com
基金资助:
国家自然科学基金(11471174);国家自然科学基金(11501110);浙江省自然科学基金(LY17A010007);宁波市自然科学基金(2018A610194)

The Non-Existence of Non-Radial Blow-Up Solutions for the Quasilinear Elliptic System

Ting Ji¹,Lianggen Hu^1,*(),Jing Zeng²

¹ Department of Mathematics, Ningbo University, Zhejiang Ningbo 315211
² School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007

Received:2017-10-12 Online:2019-04-26 Published:2019-05-05
Contact: Lianggen Hu E-mail:hulianggen@tom.com
Supported by:
the NSFC(11471174);the NSFC(11501110);the Natural Science Foundation of Zhejiang Province(LY17A010007);the Natural Science Foundation of Ningbo(2018A610194)

摘要/Abstract

摘要：

该文考虑拟线性椭圆系统

$ \begin{eqnarray*}\Delta_{p_i}u_i+\zeta_i (|x|)|\nabla u_i|^{p_i-1}=\eta_i(|x|)f_i (u_1, \cdots, u_m), \end{eqnarray*} $

其中$i=1, \cdots, m$, $p_i \ge 2$, $\zeta_i$和$\eta_i$是正连续函数, $f_i$是非负连续函数且关于每个分量是非减的.通过应用新建立的比较原理证明系统不存在非径向爆破解.

关键词: 拟线性椭圆系统, 比较原理, 非存在性, 爆破解

Abstract:

In this paper, we consider the following quasilinear elliptic system

$\begin{eqnarray*}\Delta_{p_i}u_i+\zeta_i (|x|)|\nabla u_i|^{p_i-1}=\eta_i(|x|)f_i (u_1, \cdots, u_m), \;\\mbox{in}\;\ \mathbb{R} ^N, \end{eqnarray*}$

where $i=1, \cdots, m$, $p_i\ge 2$, $\zeta_i$ and $\eta_i$ are positive continuous functions, and $f_i$ is a non-negative continuous function and nondecreasing in each component for every $i\in \{1, 2, \cdots, m\}$. After using some new comparison principle, we are able to show that the system does not admit any nonradial blow-up solutions.

Key words: Quasilinear elliptic system, Comparison principle, Nonexistence, Blow-up solution

中图分类号:

O175.25

计婷,胡良根,曾晶. 拟线性椭圆系统非径向爆破解的非存在性[J]. 数学物理学报, 2019, 39(2): 307-315.

Ting Ji,Lianggen Hu,Jing Zeng. The Non-Existence of Non-Radial Blow-Up Solutions for the Quasilinear Elliptic System[J]. Acta mathematica scientia,Series A, 2019, 39(2): 307-315.

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