High Energy Normalized Solutions for the Schrodinger Equations with Exponential Critical Growth  

具有指数临界增长的薛定谔方程的高能正规化解

作　　者：ZHANG Xiao-cang XULi-ping 张小藏;许丽萍

机构地区：[1]School of Mathematics and Statistics,Henan University of Science and Technology,Luoyang 471023,China

出　　处：《Chinese Quarterly Journal of Mathematics》2025年第1期1-19,共19页数学季刊(英文版)

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.11671403 and 11671236);Henan Provincial General Natural Science Foundation Project(Grant No.232300420113)。

摘　　要：In this paper,we study high energy normalized solutions for the following Schr?dinger equation{-Δu+V(x)u+λu=f(u),in R^(2),∫_(R^(2))|u|^(2)dx=c,where c>0,λ∈R will appear as a Lagrange multiplier,V(x)=ω|x|2 represents a trapping potential,and f has an exponential critical growth.Under the appropriate assumptions of f,we have obtained the existence of normalized solutions to the above Schr?dinger equation by introducing a variational method.And these solutions are also high energy solutions with positive energy.

关 键 词：High energy normalized solutions Schrodinger equation Trapping potential Exponential critical growth Variational method 

分 类 号：O175.29[理学—数学]