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

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  • Junjun Zhou
  • Xiangyun Hu
  • Tiaojie Xiao

Abstract

In this paper, we consider the following Kirchhoff-type problems involving critical exponent . The existence and multiplicity of positive solutions for Kirchhoff-type equations with a nonlinearity in the critical growth are studied under some suitable assumptions on and . By using the mountain pass theorem and Brézis–Lieb lemma, the existence and multiplicity of positive solutions are obtained.

Suggested Citation

  • Junjun Zhou & Xiangyun Hu & Tiaojie Xiao, 2020. "Existence and Multiplicity of Positive Solutions for Kirchhoff-Type Equations with the Critical Sobolev Exponent," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-8, January.
    • Handle: RePEc:hin:jnlmpe:3965721
    DOI: 10.1155/2020/3965721
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