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Existence and Limit Behavior of Constraint Minimizers for a Varying Non-Local Kirchhoff-Type Energy Functional

Author

Listed:
  • Xincai Zhu

    (School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China)

  • Hanxiao Wu

    (School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China)

Abstract

In this paper, we study the constrained minimization problem for an energy functional which is related to a Kirchhoff-type equation. For s = 1 , there many articles have analyzed the limit behavior of minimizers when η > 0 as b → 0 + or b > 0 as η → 0 + . When the equation involves a varying non-local term ∫ R 3 | ∇ u | 2 d x s , we give a detailed limit behavior analysis of constrained minimizers for any positive sequence { η k } with η k → 0 + . The present paper obtains an interesting result on this topic and enriches the conclusions of previous works.

Suggested Citation

  • Xincai Zhu & Hanxiao Wu, 2024. "Existence and Limit Behavior of Constraint Minimizers for a Varying Non-Local Kirchhoff-Type Energy Functional," Mathematics, MDPI, vol. 12(5), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:661-:d:1344998
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