221 citations · 455 across the 37 of their papers we have counts for
4 papers · 2 filters
On a fractional magnetic pseudorelativistic operator: properties and applications
Federico Bernini, Pietro d'Avenia
We introduce a fractional magnetic pseudorelativistic operator for a general fractional order . First we define a suitable functional setting and we prove some fundament…
Existence and dynamics of normalized solutions to Schrödinger equations with generic double-behaviour nonlinearities
Bartosz Bieganowski, Pietro d'Avenia, Jacopo Schino
We study the existence of solutions to \[ -Δu + λu = f(u) \quad \text{in } \mathbb{R}^N \] with…
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…
Between Maxwell and Born-Infeld: the presence of the magnetic field
Pietro d'Avenia, Jarosław Mederski
Our motivation is to consider an electromagnetic Lagrangian density , depending on a parameter such that, for it corresponds to the Born-Infeld Lagrangian dens…