265 citations · 815 across the 42 of their papers we have counts for
22 papers · 1 filter
NLS with mass-subcritical combined nonlinearities: small mass -scattering
Jacopo Bellazzini, Luigi Forcella, Vladimir Georgiev
We prove small data scattering in the mass-subcritical regime for the NLS equation with double nonlinearities, where a focusing leading term is perturbed by a lower order defocusin…
Mass-subcritical Half-Wave Equation with mixed nonlinearities: existence and non-existence of ground states
Jacopo Bellazzini, Luigi Forcella
We consider the problem of existence of constrained minimizers for the focusing mass-subcritical Half-Wave equation with a defocusing mass-subcritical perturbation. We show the exi…
Scattering for non-radial 3D NLS with combined nonlinearities: the interaction Morawetz approach
Jacopo Bellazzini, Van Duong Dinh, Luigi Forcella
We give a new proof of the scattering below the ground state energy level for a class of nonlinear Schrödinger equations (NLS) with mass-energy intercritical competing nonlineariti…
Dynamics of solutions to the Gross-Pitaevskii equation describing dipolar Bose-Einstein condensates
Jacopo Bellazzini, Luigi Forcella
We review some recent results on the long time dynamics of solutions to the Gross-Pitaevskii equation governing non-trapped dipolar Quantum Gases. We describe the asymptotic behavi…
Ground state energy threshold and blow-up for NLS with competing nonlinearities
Jacopo Bellazzini, Luigi Forcella, Vladimir Georgiev
We consider the nonlinear Schrödinger equation with combined nonlinearities, where the leading term is an intracritical focusing power-type nonlinearity, and the perturbation is gi…
Dynamical collapse of cylindrical symmetric Dipolar Bose-Einstein condensates
Jacopo Bellazzini, Luigi Forcella
We study the formation of singularities for cylindrical symmetric solutions to the Gross-Pitaevskii equation describing a dipolar Bose-Einstein condensate. We prove that solutions…
Finite energy traveling waves for the Gross-Pitaevskii equation in the subsonic regime
Jacopo Bellazzini, David Ruiz
In this paper we study the existence of finite energy traveling waves for the Gross-Pitaevskii equation. This problem has deserved a lot of attention in the literature, but the exi…
On Traveling Solitary Waves and Absence of Small Data Scattering for Nonlinear Half-Wave Equations
Jacopo Bellazzini, Vladimir Georgiev, Enno Lenzmann +1
We consider nonlinear half-wave equations with focusing power-type nonlinearity $$ i \pt_t u = \sqrt{-Δ} \, u - |u|^{p-1} u, \quad \mbox{with $(t,x) \in \R \times \R^d$} $$ with ex…
Traveling waves for the quartic focusing Half Wave equation in one space dimension
Jacopo Bellazzini, Vladimir Georgiev, Nicola Visciglia
We consider the quartic focusing Half Wave equation (HW) in one space dimension. We show first that that there exist traveling wave solutions with arbitrary small $H^{\frac 12}(\R)…
Long time dynamics for semirelativistic NLS and Half Wave in arbitrary dimension
Jacopo Bellazzini, Vladimir Georgiev, Nicola Visciglia
We consider the Cauchy problems associated with semirelativistc NLS (sNLS) and half wave (HW). In particular we focus on the following two main questions: local/global Cauchy theor…
Existence and Stability of standing waves for supercritical NLS with a Partial Confinement
J. Bellazzini, N. Boussaid, L. Jeanjean +1
We prove the existence of orbitally stable ground states to NLS with a partial confinement together with qualitative and symmetry properties. This result is obtained for nonlineari…
On dipolar quantum gases in the unstable regime
Jacopo Bellazzini, Louis Jeanjean
We study the nonlinear Schrödinger equation arising in dipolar Bose-Einstein condensate in the unstable regime. Two cases are studied: the first when the system is free, the second…
Sharp lower bounds for Coulomb energy
Jacopo Bellazzini, Marco Ghimenti, Tohru Ozawa
We prove lower bounds for Coulomb energy for radially symmetric functions in with . In case we show that the lo…
Multi-solitary waves for the nonlinear Klein-Gordon equation
Jacopo Bellazzini, Marco Ghimenti, Stefan Le Coz
We consider the nonlinear Klein-Gordon equation in . We call multi-solitary waves a solution behaving at large time as a sum of boosted standing waves. Our main result is the…
On the existence of hylomorphic vortices in the nonlinear Klein-Gordon equation
Jacopo Bellazzini, Vieri Benci, Claudio Bonanno +1
In this paper we prove the existence of vortices, namely standing waves with non null angular momentum, for the nonlinear Klein-Gordon equation in dimension . We show with…
Existence and instability of standing waves with prescribed norm for a class of Schrödinger-Poisson equations
Jacopo Bellazzini, Louis Jeanjean, Tingjian Luo
In this paper we study the existence and the instability of standing waves with prescribed -norm for a class of Schrödinger-Poisson-Slater equations in %orbitally sta…
On the Existence of the Fundamental Eigenvalue of an Elliptic Problem in R^N
Jacopo Bellazzini, Vieri Benci, Marco G. Ghimenti +1
We study an eigenvalue problem for functions in R^N and we find sufficient conditions for the existence of the fundamental eigenvalue. This result can be applied to the study of th…
On translation invariant constrained minimization problems with application to Schrödinger-Poisson equation
Jacopo Bellazzini, Gaetano Siciliano
In this paper we study the existence of minimizers for a class of constrained minimization problems that are invariant under translations. We call …
Stable standing waves for a class of nonlinear Schroedinger-Poisson equations
Jacopo Bellazzini, Gaetano Siciliano
We prove the existence of orbitally stable standing waves with prescribed -norm for the following Schrödinger-Poisson type equation \label{intro} %{%{ll} iψ_{t}+ Δψ- (|x|^{-1}…
Hylomorphic solitons in the nonlinear Klein-Gordon equation
J. Bellazzini, V. Benci, C. Bonanno +1
Roughly speaking a solitary wave is a solution of a field equation whose energy travels as a localised packet and which preserves this localisation in time. A soliton is a solitary…
Magneto-static vortices in two dimensional Abelian gauge theories
J. Bellazzini, C. Bonanno, G. Siciliano
We study the existence of vortices of the Klein-Gordon-Maxwell equations in the two dimensional case. In particular we find sufficient conditions for the existence of vortices in t…
Solitons for the nonlinear Klein-Gordon equation
J. Bellazzini, V. Benci, C. Bonanno +1
In this paper we study existence and orbital stability for solitary waves of the nonlinear Klein-Gordon equation. The energy of these solutions travels as a localized packet, hence…