Localization of normalized solutions for saturable nonlinear Schr?dinger equations

被引：0
作者：
Xiaoming Wang [1 ]
Zhi-Qiang Wang [2 ,3 ]
Xu Zhang [4 ]
机构：
[1] School of Mathematics & Computer Science, Shangrao Normal University
[2] College of Mathematics and Statistics, Fujian Normal University
[3] Department of Mathematics and Statistics, Utah State University
[4] School of Mathematics and Statistics, Central South University
来源：
ScienceChina(Mathematics) | 2023年 / 66卷 / 11期
基金：
中国国家自然科学基金;
关键词：
D O I：
暂无
中图分类号：
O175.29 [非线性偏微分方程];
学科分类号：
070104 ;
摘要：
In this paper,we study the existence and concentration behavior of the semiclassical states with L2-constraints for the following saturable nonlinear Schr?dinger equation:-ε2Δv+Γ(I(x)+v2)/(1+I(x)+v2)v=λv for x∈R2.For a negatively large coupling constant Γ,we show that there exists a family of normalized positive solutions(i.e.,with the L2-constraint) when ε is small,which concentrate around local maxima of the intensity function I(x) as ε→0.We also consider the case where I(x) may tend to-1 at infinity and the existence of multiple solutions.The proof of our results is variational and the novelty of the work lies in the development of a new truncation-type method for the construction of the desired solutions.
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页码：2495 / 2522
页数：28
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