On radial positive normalized solutions of the Nonlinear Schrödinger equation in an annulus

被引：2

作者：

Liang, Jian ^{[1
,2
]}

Song, Linjie ^{[1
,2
,3
]}

机构：

[1] Acad Sinica, AMSS, Inst Math, Beijing 100190, Peoples R China

[2] Univ Chinese Acad Sci, Beijing 100049, Peoples R China

[3] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2024年 / 31卷 / 02期

关键词：

Normalized solutions; Orbital stability; Nonlinear Schrodinger equations; Annulus; UNIQUENESS; EXISTENCE;

D O I：

10.1007/s00030-023-00917-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We are interested in the following semilinear elliptic problem: { -Delta u+lambda u=u(p-1),x is an element of T, u>0,u=0on partial derivative T, integral(T)u(2)dx= cwhere T={x is an element of R-N:1<|x|<2}is an annulus inRN,N >= 2,p>1isSobolev-subcritical, searching for conditions (aboutc,Nandp) for the existence of positive radial solutions. We analyze the asymptotic behaviorofcas lambda ->+infinity and lambda ->-lambda 1to get the existence, non-existence and multiplicity of normalized solutions. Additionally, based on the properties of these solutions, we extend the results obtained in Pierotti et al. in CalcVar Partial Differ Equ 56:1-27, 2017. In contrast of the earlier results, a positive radial solution with arbitrarily large mass can be obtained whenN >= 3orifN= 2 and p<6. Our paper also includes the demonstrationof orbital stability/instability results.

引用

页数：14

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