463 citations · 801 across the 24 of their papers we have counts for
28 papers
Schrödinger equation in dimension two with competing logarithmic self-interaction
Antonio Azzollini, Pietro d'Avenia, Alessio Pomponio
In this paper we study the equation \[ -Δu +(\log |\cdot|*|u|^2)u=(\log|\cdot|*|u|^q)|u|^{q-2}u, \qquad \hbox{ in }\mathbb{R}^2, \] where . By means of variational arg…
The 2-dimensional nonlinear Schrodinger-Maxwell system
Antonio Azzollini, Marcos Tadeu de Oliveira Pimenta
In this paper we carry on the study of a system recently introduced by the first author as the planar version of the well known electrostatic Schrödinger - Maxwell equations. In th…
The planar Schrödinger-Poisson system with a positive potential
Antonio Azzollini
In this paper we consider the problem \begin{equation*} \left \{ \begin{array}{l} -Δu \pm ϕu + W'(x,u) = 0\hbox{ in } \mathbb{R}^2,\newline Δϕ= u^2 \hbox{ in } \mathbb{R}^2, \end{a…
Finite energy standing waves for the Klein-Gordon-Maxwell system: the limit case
Antonio Azzollini
In this paper we consider the Klein-Gordon-Maxwell system in the electrostatic case, assuming the fall-off large-distance requirement on the gauge potential. We are interested in p…
Positive energy static solutions for the Chern-Simons-Schrödinger system under a large-distance fall-off requirement on the gauge potentials
Antonio Azzollini, Alessio Pomponio
In this paper we prove the existence of a positive energy static solution for the Chern-Simons-Schrödinger system under a large-distance fall-off requirement on the gauge potential…
On the Schrödinger-Born-Infeld system
Antonio Azzollini, Alessio Pomponio, Gaetano Siciliano
In this paper we study a system which we propose as a model to describe the interaction between matter and electromagnetic field from a dualistic point of view. This system arises…