Stability of the standing waves of the concentrated NLSE in dimension two

被引：8

作者：

Adami, Riccardo ^{[1
]}

Carlone, Raffaele ^{[2
]}

Correggi, Michele ^{[3
]}

Tentarelli, Lorenzo ^{[1
]}

机构：

[1] Politecn Torino, Dipartimento Sci Matemat GL Lagrange, Corso Duca Abruzzi 24, I-10129 Turin, Italy

[2] Univ Napoli Federico II, Dipartimento Matemat & Applicaz R Caccioppoli, MSA, Via Cinthia, I-80126 Naples, Italy

[3] Politecn Milan, Dipartimento Matemat, Piazza Leonardo da Vinci 32, I-20133 Milan, Italy

来源：

MATHEMATICS IN ENGINEERING | 2021年 / 3卷 / 02期

关键词：

nonlinear Schrodinger equation; point interactions; standing waves; orbital stability; NONLINEAR SCHRODINGER-EQUATION; BLOW-UP; GROUND-STATES; SYSTEMS;

D O I：

10.3934/mine.2021011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we will continue the analysis of two dimensional Schrodinger equation with a fixed, pointwise, nonlinearity started in [2, 13]. In this model, the occurrence of a blow-up phenomenon has two peculiar features: the energy threshold under which all solutions blow up is strictly negative and coincides with the infimum of the energy of the standing waves; there is no critical power nonlinearity, i.e., for every power there exist blow-up solutions. Here we study the stability properties of stationary states to verify whether the anomalies mentioned before have any counterpart on the stability features.

引用

页数：15

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