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math.AP2018
Equilibrium measures and equilibrium potentials in the Born-Infeld model
Denis Bonheure, Pietro d'Avenia, Alessio Pomponio +1
In this paper, we consider the electrostatic Born-Infeld model \begin{equation*} \tag{} \left\{ \begin{array}{rcll} -\operatorname{div}\left(\displaystyle\frac{\nabla…
math.AP2018
Standing waves for a Schrödinger-Chern-Simons-Higgs system
Pietro d'Avenia, Alessio Pomponio
We consider a system arising from a nonrelativistic Chern-Simon-Higgs model, in which a charged field is coupled with a gauge field. We prove an existence result for small coupling…
math.AP2018
Nonlinear Schrödinger equation in the Bopp-Podolsky electrodynamics: solutions in the electrostatic case
Pietro d'Avenia, Gaetano Siciliano
We study the following nonlinear Schrödinger-Bopp-Podolsky system \[ \begin{cases} -Δu + ωu + q^{2}ϕu = |u|^{p-2}u -Δϕ+ a^2 Δ^2 ϕ= 4πu^2 \end{cases} \hbox{ in }\mathbb{R}^3 \] with…