27 citations · 178 across the 25 of their papers we have counts for
17 papers · 1 filter
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…
On the nodal set of solutions to Dirac equations
William Borrelli, Ruijun Wu
Motivated by various geometric problems, we study the nodal set of solutions to Dirac equations on manifolds, of general form. We prove that such set has Hausdorff dimension less t…
Uniqueness of the critical point for solutions to some -Laplace equations in the plane
William Borrelli, Sunra Mosconi, Marco Squassina
We prove that quasi-concave positive solutions to a class of quasi-linear elliptic equations driven by the -Laplacian in convex bounded domains of the plane have only one critic…
Concavity properties for solutions to -Laplace equations with concave nonlinearities
William Borrelli, Sunra Mosconi, Marco Squassina
We obtain new concavity results, up to a suitable transformation, for a class of quasi-linear equations in a convex domain involving the -Laplace operator and a general nonlinea…
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…
On the continuum limit for a model of binary waveguide arrays
William Borrelli
In this paper we prove the convergence of solutions to discrete models for binary waveguide arrays toward those of their formal continuum limit, for which we also show the existenc…
Bifurcating standing waves for effective equations in gapped honeycomb structures
William Borrelli, Raffaele Carlone
In this paper we deal with two dimensional cubic Dirac equations appearing as effective model in gapped honeycomb structures. We give a formal derivation starting from cubic Schröd…
Symmetric solutions for a 2D critical Dirac equation
William Borrelli
In this paper we show the existence of infinitely many symmetric solutions for a cubic Dirac equation in two dimensions, which appears as effective model in systems related to hone…
Some properties of Dirac-Einstein bubbles
William Borrelli, Ali Maalaoui
We prove smoothness and provide the asymptotic behavior at infinity of solutions of Dirac-Einstein equations on , which appear in the bubbling analysis of conformal D…
Ground state Dirac bubbles and Killing spinors
William Borrelli, Andrea Malchiodi, Ruijun Wu
We prove a classification result for ground state solutions of the critical Dirac equation on , . By exploiting its conformal covariance, the equation can be…
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…
Sharp decay estimates for critical Dirac equations
William Borrelli, Rupert L. Frank
We prove sharp pointwise decay estimates for critical Dirac equations on with . They appear for instance in the study of critical Dirac equations on compact…
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.…
Weakly localized states for nonlinear Dirac equations
William Borrelli
We prove the existence of infinitely many non square-integrable stationary solutions for a family of massless Dirac equations in 2D. They appear as effective equations in two dimen…
Multiple solutions for a self-consistent Dirac equation in two dimensions
William Borrelli
This paper is devoted to the variational study of an effective model for the electron transport in a graphene sample. We prove the existence of infinitely many stationary solutions…