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.

引用

页码：2495 / 2522

页数：28

共 31 条

[1] Chengxiang Zhang,Zhi-Qiang Wang.Concentration of nodal solutions for logarithmic scalar field equations[J].Journal de mathématiques pures et appliquées,2020
[2] Lin Tai Chia,Wu Tsung Fang.Multiple positive solutions of saturable nonlinear Schrödinger equations with intensity functions[J].Discrete & Continuous Dynamical Systems - A,2020
[3] Xiangqing Liu,Jiaquan Liu,Zhi-Qiang Wang.Localized nodal solutions for quasilinear Schrödinger equations[J].Journal of Differential Equations,2019
[4] Xiaoming Wang,Tai-Chia Lin,Zhi-Qiang Wang.Existence and concentration of ground states for saturable nonlinear Schr?dinger equations with intensity functions in R 2[J].Nonlinear Analysis,2018
[5] Oscillating solutions for nonlinear Helmholtz equations
Rainer Mandel
Eugenio Montefusco
Benedetta Pellacci
[J]. Zeitschrift für angewandte Mathematik und Physik, 2017, 68
[6] Tai-Chia Lin,Milivoj R. Beli?,Milan S. Petrovi?,Hichem Hajaiej,Goong Chen.The virial theorem and ground state energy estimates of nonlinear Schr?dinger equations in $$\mathbb {R}^2$$ with square root and saturable nonlinearities in nonlinear optics[J].Calculus of Variations and Partial Differential Equations,2017(5)
[7] Tai-Chia Lin,Xiaoming Wang,Zhi-Qiang Wang.Orbital stability and energy estimate of ground states of saturable nonlinear Schr?dinger equations with intensity functions in[formula omitted][J].Journal of Differential Equations,2017(8)
[8] Localized nodal solutions of higher topological type for semiclassical nonlinear Schrödinger equations
Shaowei Chen
Zhi-Qiang Wang
[J]. Calculus of Variations and Partial Differential Equations, 2017, 56
[9] Liliane A. Maia,Eugenio Montefusco,Benedetta Pellacci.Singularly perturbed elliptic problems with nonautonomous asymptotically linear nonlinearities[J].Nonlinear Analysis,2015
[10] Tai-Chia Lin,Milivoj R. Beli??,Milan S. Petrovi??,Goong Chen.Ground states of nonlinear Schr??dinger systems with saturable nonlinearity in R2 for two counterpropagating beams[J].Journal of Mathematical Physics,2014(1)

← 1 2 3 4 →