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

Ji Lei1, Liao Jiafeng2   

  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 Revised:2018-11-22 Online:2019-10-26 Published:2019-11-08
  • Supported by:
    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) and the Innovative Research Team of China West Normal University (CXTD2018-8)

Abstract: The following nonhomogeneous Kirchhoff type equations with critical exponent

where Ω is a smooth bounded domain in R3, a, b, λ > 0 are parameters and fL6/5 (Ω) 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