Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (5): 1094-1101.

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Existence of the Second Positive Solution for a Class of Nonhomogeneous Kirchhoff Type Problems with Critical Exponent

Lei Ji1(),Jiafeng Liao2,*()   

  1. 1 College of Mathematics and Science, Jingzhong University, Shanxi Jingzhong 030600
    2 College of Mathematics Education, China West Normal University, Sichuan Nanchong 637002
  • Received:2018-08-29 Online:2019-10-26 Published:2019-11-08
  • Contact: Jiafeng Liao;
  • Supported by:
    the Scientific Research Fund of Sichuan Provincial Education Department(18ZA0471);the Meritocracy Research Funds of China West Normal University(17YC383);the Fundamental Research Funds of China West Normal University(18B015);the Innovative Research Team of China West Normal University(CXTD2018-8)


The following nonhomogeneous Kirchhoff type equations with critical exponent

where $\Omega$ is a smooth bounded domain in ${\Bbb R} ^{3}, $ $a, b, \lambda>0$ are parameters and $f\in L^{\frac{6}{5}}(\Omega)$ is nonzero and nonnegative, are considered. By the variational method, the second positive solution is obtained which completes and improves the resulsts of [3] and [5].

Key words: Kirchhoff equation, Critical exponent, Variational method, Positive solution

CLC Number: 

  • O177.25