57 citations · 475 across the 30 of their papers we have counts for
8 papers · 1 filter
-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…
Nonlinear Dirac Equation On Graphs With Localized Nonlinearities: Bound States And Nonrelativistic Limit
William Borrelli, Raffaele Carlone, Lorenzo Tentarelli
In this paper we study the nonlinear Dirac (NLD) equation on noncompact metric graphs with localized Kerr nonlinearities, in the case of Kirchhoff-type conditions at the vertices.…
Nonlinear singular perturbations of the fractional Schrödinger equation in dimension one
Raffaele Carlone, Domenico Finco, Lorenzo Tentarelli
The paper discusses nonlinear singular perturbations of delta type of the fractional Schrödinger equation , with …
An introduction to the two-dimensional Schrödinger equation with nonlinear point interactions
R Carlone, M Correggi, L Tentarelli
We present an introduction to the nonlinear Schrödinger equation (NLSE) with concentrated nonlinearities in . Precisely, taking a cue from the linear problem, we sket…
On the extensions of the De Giorgi approach to nonlinear hyperbolic equations
Lorenzo Tentarelli
In this talk we present an overview on the extensions of the De Giorgi approach to general second order nonlinear hyperbolic equations. We start with an introduction to the origina…
An existence result for dissipative nonhomogeneous hyperbolic equations via a minimization approach
Lorenzo Tentarelli, Paolo Tilli
We discuss a purely variational approach to the study of a wide class of second order nonhomogeneous dissipative hyperbolic PDEs. Precisely, we focus on the wave-like equations tha…
Ground states of the -critical NLS equation with localized nonlinearity on a tadpole graph
Simone Dovetta, Lorenzo Tentarelli
The paper aims at giving a first insight on the existence/nonexistence of ground states for the -critical NLS equation on metric graphs with localized nonlinearity. In particu…