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Multiplicity of Solutions for Fourth-Order Elliptic Equations of Kirchhoff Type with Critical Exponent

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Abstract

In this paper, we deal with fourth-order elliptic equations of Kirchhoff type with critical exponent in bounded domains, the new results about existence, and multiplicity of solutions are obtained by using the concentration-compactness principle and variational method.

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Acknowledgment

The authors would like to thank the anonymous referees for their suggestions and helpful comments which improved the presentation of the original manuscript.

The first author is supported by the National Natural Science Foundation of China (Grant No.11301038), the Natural Science Foundation of Jilin Province (Grant No.20160101244JC), the open project program of Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University(Grant no. 93K172013K03).

The second author is supported by NSFC Grant (No. 11371166) and 985 Project of Jilin University.

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Authors and Affiliations

  1. College of Mathematics, Jilin University, Changchun, 130012, People’s Republic of China

    Yueqiang Song & Shaoyun Shi

  2. Scientific Research Department, Changchun Normal University, Changchun, 130032, Jilin, People’s Republic of China

    Yueqiang Song

  3. State Key Laboratory of Automotive Simulation and Control, Changchun, 130012, People’s Republic of China

    Shaoyun Shi

Authors
  1. Yueqiang Song
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  2. Shaoyun Shi
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Correspondence to Yueqiang Song.

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Song, Y., Shi, S. Multiplicity of Solutions for Fourth-Order Elliptic Equations of Kirchhoff Type with Critical Exponent. J Dyn Control Syst 23, 375–386 (2017). https://doi.org/10.1007/s10883-016-9331-x

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  • DOI: https://doi.org/10.1007/s10883-016-9331-x

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