Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (2): 307-315.

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

Ting Ji1,Lianggen Hu1,*(),Jing Zeng2   

  1. 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)

Abstract:

In this paper, we consider the following quasilinear elliptic system

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

CLC Number: 

  • O175.25
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