Acta mathematica scientia,Series A ›› 2026, Vol. 46 ›› Issue (4): 1420-1427.

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On the Existence and Concentration of Minimizers for a Class of Constrained Variational Problems in Three Dimensional Space

Na Ba1(), Kairui Zhou2(), Xiaoyu Zeng2,*()   

  1. 1 School of Science, Hubei University of Technology, Wuhan 430068
    2 School of Mathematics and Statistics, Wuhan University of Technology, Wuhan 430070
  • Received:2025-12-25 Revised:2026-02-06 Online:2026-08-26 Published:2026-06-10
  • Contact: Xiaoyu Zeng E-mail:bana1002@126.com;zkr_20060222@qq.com;xyzeng@whut.edu.cn
  • Supported by:
    Key Scientific Research Project of Hubei Provincial Department of Education(D20181405);NSFC(12322106);NSFC(12171379)

Abstract:

In this paper, we employ the constrained variational method to investigate the optimal parameter range for the existence and non-existence of ground states to a class of Schrödinger equations with inhomogeneous terms in three-dimensional space, and discusses the mass concentration behavior of the ground states with respect to the variation of the parameter.

Key words: constrained variation, ground states, energy estimation, concentration behavior

CLC Number: 

  • O175.25
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