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

doi:10.1007/s10473-024-0312-y

Acta mathematica scientia,Series B ›› 2024, Vol. 44 ›› Issue (3): 984-996.doi: 10.1007/s10473-024-0312-y

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

Bin Chen, Yongshuai Gao^*, Yujin Guo, Yue Wu

School of Mathematics and Statistics, Hubei key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, China

Received:2023-03-09 Revised:2023-10-05 Online:2024-06-25 Published:2024-05-21
Contact: *Yongshuai Gao, ysgao@mails.ccnu.edu.cn.
About author:Bin Chen,E-mail:binchenmath@mails.ccnu.edu.cn; Yujin Guo, yguo@ccnu.edu.cn; Yue Wu, yuewu627@163.com
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

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.

Key words: decaying nonlinearity, $L^2$-subcritical, minimizers, bounded domains, mass concentration

CLC Number:

35J20

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.

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

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