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…