57 citations · 475 across the 30 of their papers we have counts for
31 papers
Normalized nonlinear Schrödinger ground states on defected grids with unbounded defects
William Borrelli, Nicolò Cangiotti, Simone Dovetta +1
We study normalized ground states for the nonlinear Schrödinger energy on two-dimensional square grids with unbounded defects. We first show that unbounded defects do not necessari…
Dirac solitons in one-dimensional nonlinear Schrödinger equations
William Borrelli, Elena Danesi, Simone Dovetta +1
In this paper we study a family of one-dimensional stationary cubic nonlinear Schrödinger (NLS) equations with periodic potentials and linear part displaying Dirac points in the di…
Doubly nonlinear Schrödinger normalized ground states on 2D grids: existence results and singular limits
Daniele Barbera, Filippo Boni, Simone Dovetta +1
We investigate the existence and the singular limit of normalized ground states for focusing doubly nonlinear Schrödinger equations with both standard and concentrated nonlineariti…
Normalized solutions of one-dimensional defocusing NLS equations with nonlinear point interactions
Daniele Barbera, Filippo Boni, Simone Dovetta +1
We investigate normalized solutions for doubly nonlinear Schrödinger equations on the real line with a defocusing standard nonlinearity and a focusing nonlinear point interaction o…
Non-uniqueness of normalized NLS ground states on polygons with homogeneous Neumann boundary conditions
Simone Dovetta, Enrico Serra, Lorenzo Tentarelli
We provide a non-uniqueness result for normalized ground states of nonlinear Schrödinger equations with pure power nonlinearity on polygons with homogeneous Neumann boundary condit…
The search for NLS ground states on a hybrid domain: Motivations, methods, and results
Riccardo Adami, Filippo Boni, Raffaele Carlone +1
We discuss the problem of establishing the existence of the Ground States for the subcritical focusing Nonlinear Schrödinger energy on a domain made of a line and a plane intersect…
NLS ground states on a hybrid plane
Riccardo Adami, Filippo Boni, Raffaele Carlone +1
We study existence, nonexistence, and qualitative properties of ground states for a focusing, subcritical Nonlinear Schrödinger Equation on a hybrid plane, consisting of a half-lin…
A general review on the NLS equation with point-concentrated nonlinearity
Lorenzo Tentarelli
The paper presents a complete (to the best of the author's knowledge) overview on the existing literature concerning the NLS equation with point-concentrated nonlinearity. Precisel…
Well-posedness of the three-dimensional NLS equation with sphere-concentrated nonlinearity
Domenico Finco, Lorenzo Tentarelli, Alessandro Teta
We discuss strong local and global well-posedness for the three-dimensional NLS equation with nonlinearity concentrated on . Precisely, local well-posedness is proved…
Existence, structure, and robustness of ground states of a NLSE in 3D with a point defect
Riccardo Adami, Filippo Boni, Raffaele Carlone +1
We study the ground states for the Schrödinger equation with a focusing nonlinearity and a point interaction in dimension three. We establish that ground states exist for every val…
Ground states for the planar NLSE with a point defect as minimizers of the constrained energy
Riccardo Adami, Filippo Boni, Raffaele Carlone +1
We investigate the ground states for the focusing, subcritical nonlinear Schrödinger equation with a point defect in dimension two, defined as the minimizers of the energy function…
Complete ionization for a non-autonomous point interaction model in d = 2
William Borrelli, Raffaele Carlone, Lorenzo Tentarelli
We consider the two dimensional Schrödinger equation with time dependent delta potential, which represents a model for the dynamics of a quantum particle subject to a point interac…
Symmetry breaking in two-dimensional square grids: persistence and failure of the dimensional crossover
Simone Dovetta, Lorenzo Tentarelli
We discuss the model robustness of the infinite two-dimensional square grid with respect to symmetry breakings due to the presence of defects, that is, lacks of finitely or infinit…
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…
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…