MULTIPLE NORMALIZED SOLUTIONS FOR A QUASI-LINEAR SCHRODINGER EQUATION VIA DUAL APPROACH

被引：4

作者：

Zhang, Lin ^{[1
]}

Li, Yongqing ^{[1
]}

Wang, Zhi-qiang ^{[1
,2
]}

机构：

[1] Fujian Normal Univ, Sch Math & Stat, Fujian 350000, Peoples R China

[2] Utah State Univ, Dept Math & Stat, Logan, UT 84322 USA

来源：

TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS | 2023年 / 61卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Quasi-linear Schrodinger equations; normalized solutions; dual method; the minimax principle; SCALAR FIELD-EQUATIONS; CONCENTRATION-COMPACTNESS PRINCIPLE; ELLIPTIC-EQUATIONS; SOLITON-SOLUTIONS; STANDING WAVES; EXISTENCE; STABILITY; CALCULUS;

D O I：

10.12775/TMNA.2022.052

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we construct multiple normalized solutions of the following from quasi-linear Schrodinger equation: -Delta u - Delta(|u|(2))u- mu u = |u|(p-2)u, in R-N, subject to a mass-sub critical constraint. In order to overcome non-smoothness of the associated variational formulation we make use of the dual approach. The constructed solutions possess energies being clustered at 0 level which makes it difficult to use existing methods for non-smooth variational problems such as the variational perturbation approach.

引用

页码：465 / 489

页数：25

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