Acta mathematica scientia,Series A ›› 2017, Vol. 37 ›› Issue (6): 1119-1124.

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Existence and Multiplicity of Positive Solutions for the Superlinear Kirchhoff-Type Equations with Critical Sobolev Exponent

Liao Jiafeng1,2, Li Hongying1   

  1. 1 School of Mathematics and Information, China West Normal University, Sichuan Nanchong 637002;
    2 College of Mathematical Sciences, Zunyi Normal College, Guizhou Zunyi 563002
  • Received:2016-09-13 Revised:2017-04-15 Online:2017-12-26 Published:2017-12-26
  • Supported by:
    Supported by the NSFC (11471267), the Natural Science Foundation of Education of Guizhou Province (KY[2016]046) and the Doctoral Scientific Research Foundation of China West Normal University (16E014)

Abstract: In this paper, we consider a class of superlinear Kirchhoff-type problems with Sobolev critical exponent. Using the variational method, we obtain the existence and multiplicity of positive solutions. Moreover, a global (PS) condition is obtained for this critical problem.

Key words: Kirchhoff-type equation, Critical exponent, Positive solutions, Variational method, (PS) condition

CLC Number: 

  • O175.25
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