ZHANG Yue.Existence of Standing Waves for the Nonlinear Schrödinger Equation with Energy Critical Growth[J].Journal of Chengdu University of Information Technology,2024,39(03):369-373.[doi:10.16836/j.cnki.jcuit.2024.03.015]
具有能量临界增长的非线性薛定谔方程驻波的存在性
- Title:
- Existence of Standing Waves for the Nonlinear Schrödinger Equation with Energy Critical Growth
- 文章编号:
- 2096-1618(2024)03-0369-05
- Keywords:
- nonlinear Schrödinger equation; energy critical growth; ground state standing wave; variational problem; existence
- 分类号:
- O175.29
- 文献标志码:
- A
- 摘要:
- 提出一类具有能量临界增长的非线性薛定谔方程,满足非线性项均为聚焦状态。通过解决一个在给定的条件下变分问题,得到该类方程基态驻波解的存在性。结果表明,当空间维数大于4时,基态驻波解对于所有的正频率都是存在的。
- Abstract:
- Firstly, a class of nonlinear Schröodinger equation with energy critical growth is proposed in this paper, which meets the condition that the nonlinear terms are all focusing. Next, by solving a variational problem under given conditions, the existence of the ground state standing wave solution of this kind of equation is verified. The results show that the ground state standing wave solution exists for all positive frequencies when the dimension of space is not less than four.
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备注/Memo
收稿日期:2022-12-30