9 citations · 9 across the 1 of their papers we have counts for
11 papers
Stability of the standing waves of the concentrated NLSE in dimension two
Riccardo Adami, Raffaele Carlone, Michele Correggi +1
In this paper we will continue the analysis of two dimensional Schrödinger equation with a fixed, pointwise, nonlinearity started in [2, 13]. In this model, the occurrence of a blo…
On the nonlinear Dirac equation on noncompact metric graphs
William Borrelli, Raffaele Carlone, Lorenzo Tentarelli
The paper discusses the Nonlinear Dirac Equation with Kerr-type nonlinearity (i.e., ) on noncompact metric graphs with a finite number of edges, in the case of Kirchhoff-…
A note on the Dirac operator with Kirchoff-type vertex conditions on noncompact metric graphs
William Borrelli, Raffaele Carlone, Lorenzo Tentarelli
In this note we present some properties of the Dirac operator on noncompact metric graphs with Kirchoff-type vertex conditions. In particular, we discuss the specific features of t…
An overview on the standing waves of nonlinear Schrödinger and Dirac equations on metric graphs with localized nonlinearity
William Borrelli, Raffaele Carlone, Lorenzo Tentarelli
We present a brief overview on the existence/nonexistence of standing waves for the NonLinear Schrödinger and the NonLinear Dirac Equations (NLSE/NLDE) on metric graphs with locali…
-critical NLS on noncompact metric graphs with localized nonlinearity: topological and metric features
Simone Dovetta, Lorenzo Tentarelli
Carrying on the discussion initiated in (Dovetta-Tentarelli'18), we investigate the existence of ground states of prescribed mass for the -critical NonLinear Schrödinger Equat…
Blow-up for the pointwise NLS in dimension two: absence of critical power
Riccardo Adami, Raffaele Carlone, Michele Correggi +1
We consider the Schrödinger equation in dimension two with a fixed, pointwise, focusing nonlinearity and show the occurrence of a blow-up phenomenon with two peculiar features: fir…