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On Kirchhoff-Type Equations with Hardy Potential and Berestycki–Lions Conditions

Author

Listed:
  • Hua Yang

    (School of Mathematics and Information Science, Anyang Institute of Technology, Anyang 455000, China)

  • Jiu Liu

    (School of Mathematics and Statistics, Qiannan Normal University for Nationalities, Duyun 558000, China
    Key Laboratory of Complex Systems and Intelligent Optimization of Guizhou Province, Duyun 558000, China)

Abstract

The purpose of this paper is to investigate the existence and asymptotic properties of solutions to a Kirchhoff-type equation with Hardy potential and Berestycki–Lions conditions. Firstly, we show that the equation has a positive radial ground-state solution u λ by using the Pohozaev manifold. Secondly, we prove that the solution u λ n , up to a subsequence, converges to a radial ground-state solution of the corresponding limiting equations as λ n → 0 − . Finally, we provide a brief summary.

Suggested Citation

  • Hua Yang & Jiu Liu, 2023. "On Kirchhoff-Type Equations with Hardy Potential and Berestycki–Lions Conditions," Mathematics, MDPI, vol. 11(12), pages 1-10, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2648-:d:1167996
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