数学
匡威
紧凑空间
指数增长
拉格朗日乘数
背景(考古学)
类型(生物学)
指数函数
约束(计算机辅助设计)
薛定谔方程
乘数(经济学)
数学分析
应用数学
数学优化
几何学
古生物学
生态学
宏观经济学
经济
生物
作者
Sitong Chen,Vicenţiu D. Rădulescu,Xianhua Tang,Shuai Yuan
出处
期刊:Siam Journal on Mathematical Analysis
[Society for Industrial and Applied Mathematics]
日期:2023-11-09
卷期号:55 (6): 7704-7740
被引量:8
摘要
For any , we study the existence of normalized solutions and ground state solutions to the following Schrödinger equation with -constraint: where is a Lagrange multiplier, the potential satisfies and appears as a converse direction of the Rabinowitz-type trapping potential, and the reaction enjoys critical exponential growth of Trudinger–Moser type. Under two different kinds of assumptions on , we prove several new existence results, which, in the context of normalized solutions, can be considered as both counterparts of planar unconstrained critical problems and extensions of unconstrained Schrödinger problems with Rabinowitz-type trapping potential. Especially, in this scenario, we develop some sharp estimates of energy levels and ingenious analysis techniques to restore the compactness which are novel even for constant. We believe that these techniques will allow not only treating other -constrained problems in the Trudinger–Moser critical setting but also generalizing previous results to the case of variable potentials.
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