REMARKS ON NORMALIZED GROUND STATES OF SCHRÖDINGER EQUATION WITH AT LEAST MASS CRITICAL NONLINEARITY

Yanyan Liu; Leiga Zhao

doi:10.11948/20230139

2023 Volume 13 Issue 6

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Yanyan Liu, Leiga Zhao. REMARKS ON NORMALIZED GROUND STATES OF SCHRÖDINGER EQUATION WITH AT LEAST MASS CRITICAL NONLINEARITY[J]. Journal of Applied Analysis & Computation, 2023, 13(6): 3524-3534. doi: 10.11948/20230139

Citation:

Yanyan Liu, Leiga Zhao. REMARKS ON NORMALIZED GROUND STATES OF SCHRÖDINGER EQUATION WITH AT LEAST MASS CRITICAL NONLINEARITY[J]. Journal of Applied Analysis & Computation, 2023, 13(6): 3524-3534. doi: 10.11948/20230139

REMARKS ON NORMALIZED GROUND STATES OF SCHRÖDINGER EQUATION WITH AT LEAST MASS CRITICAL NONLINEARITY

Yanyan Liu^1,,
Leiga Zhao^1, ,

1.
School of Mathematics and Statistics, Beijing Technology and Business University, Beijing, China

Author Bio: Email: liuyanyan@amss.ac.cn(Y. Liu)
Corresponding author: Email: zhaoleiga@163.com(L. Zhao)
Fund Project: The authors were supported by National Natural Science Foundation of China (Nos. 12101020, 12171014)

Abstract

Abstract

We are concerned with the nonlinear Schrödinger equation

$ \begin{equation*}-\Delta u+\lambda u=g(u)\text{ in }\mathbb{R}^{N}\text{, }\lambda \in\mathbb{R}, \end{equation*} $

with prescribed $L^{2}$-norm $\int_{\mathbb{R}^{N}}u^{2}dx=\rho ^{2}$. Under general assumptions about the nonlinearity which allows at least mass critical growth, we prove the existence of a ground state solution to the problem via a clear constrained minimization method.
- Schrödinger equation /
- normalized ground states /
- general nonlinearities /
- minimization methods
MSC: 35B38, 35J20, 35J60, 35P30

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References

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