Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (2): 418-426.

Previous Articles     Next Articles

Existence of Positive Ground State Solutions for a Class of Kirchhoff Type Problems with Critical Exponent

Lei Ji1(),Jiafeng Liao2,*()   

  1. 1 Department of Mathematics, Jingzhong University, Shanxi Jingzhong 030600
    2 College of Mathematics Education, China West Normal University, Sichuan Nanchong 637002
  • Received:2020-10-28 Online:2022-04-26 Published:2022-04-18
  • Contact: Jiafeng Liao E-mail:jilei@jzxy.edu.cn;liaojiafeng@163.com
  • Supported by:
    the Scientific Research Fund of Sichuan Provincial Education Department(18ZA0471);the Fundamental Research Funds of China West Normal University(18B015);the Innovative Research Team of China West Normal University(CXTD2018-8)

Abstract:

The following Kirchhoff type equations with critical exponent where $\Omega\subset\mathbb{R} ^{N}(N\geq3)$ is a smooth bounded domain with smooth boundary $\partial\Omega, $ $a, \lambda>0, $$b\geq0, $ $ 0 < m < \frac{2}{N-2}, 2 < q < 2m+2, 2^{\ast}=\frac{2N}{N-2}$ are parameters, are considered. By using the Moutain-Pass Theorem, the existence positive solutions is obtained. Moreover, the existence positive ground state solutions is obtained by the Nehari method. Our result completes and improves the recent corresponding results in the literature.

Key words: Kirchhoff type problem, Critical exponent, Mountain-Pass Theorem, Nehari method, Positive ground state solution

CLC Number: 

  • O177.91
Trendmd