Stability of the standing waves of the concentrated NLSE in dimension two
Riccardo Adami, Raffaele Carlone, Michele Correggi, Lorenzo Tentarelli, <sup>†</sup><b>This contribution is part of the Special Issue:</b> Nonlinear models in applied mathematics, Guest Editor: Giuseppe Maria Coclite, Link: <a href="www.aimspress.com/mine/article/5512/special-articles" target="_blank">www.aimspress.com/mine/article/5512/special-articles
Abstract
In this paper we will continue the analysis of two dimensional Schr?dinger 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.