MINIMIZERS OF $L^2$-SUBCRITICAL VARIATIONAL PROBLEMS WITH SPATIALLY DECAYING NONLINEARITIES IN BOUNDED DOMAINS

  • Bin Chen ,
  • Yongshuai Gao ,
  • Yujin Guo ,
  • Yue Wu
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  • School of Mathematics and Statistics, Hubei key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, China
Bin Chen,E-mail:binchenmath@mails.ccnu.edu.cn; Yujin Guo, yguo@ccnu.edu.cn; Yue Wu, yuewu627@163.com

Received date: 2023-03-09

  Revised date: 2023-10-05

  Online published: 2024-05-21

Supported by

Gao's work was supported by the Graduate Education Innovation Funds (2022CXZZ088) at Central China Normal University in China; Guo's work was supported by the NSFC (12225106, 11931012) and the Fundamental Research Funds (CCNU22LJ002) for the Central Universities in China.

Abstract

This paper is concerned with the minimizers of $L^2$-subcritical constraint variational problems with spatially decaying nonlinearities in a bounded domain $\Omega$ of $\mathbb{R}^{N}$ ($N\ge 1$). We prove that the problem admits minimizers for any $M>0$. Moreover, the limiting behavior of minimizers as $M\to\infty$ is also analyzed rigorously.

Cite this article

Bin Chen , Yongshuai Gao , Yujin Guo , Yue Wu . MINIMIZERS OF $L^2$-SUBCRITICAL VARIATIONAL PROBLEMS WITH SPATIALLY DECAYING NONLINEARITIES IN BOUNDED DOMAINS[J]. Acta mathematica scientia, Series B, 2024 , 44(3) : 984 -996 . DOI: 10.1007/s10473-024-0312-y

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