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

Xincai Zhu () and Hanxiao Wu
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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

Mathematics, 2024, vol. 12, issue 5, 1-14

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.

Keywords: Kirchhoff-type energy functional; constraint minimizer; limit behavior; varying non-local term (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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