Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (3): 723-728.

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

Xiaoyao Jia(),Zhenluo Lou*()   

  1. 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;
  • 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)


In this paper, we study the following elliptic system 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

CLC Number: 

  • O175.25