Lorenzo Pisani

Solitons and the electromagnetic field

In a recent paper [4], it has been introduced a Lorentz invariant equation in three space dimensions, having soliton like solutions. We recall that, roughly speaking, a soliton is a solution whose energy travels as a localized packet and which preserves this form of localization under small perturbations (see [6], [15], [13], [10]). The equation introduced in [4] is the Euler Lagrange equation of an action functional

Note on a Schrödinger–Poisson system in a bounded domain

Abstract This work is concerned with a nonlinear system of Schrodinger–Poisson equations in a bounded domain with Dirichlet boundary conditions. We prove the existence of infinitely many solutions u ( x ) e − i ω t , for every value of ω , in equilibrium with the electrostatic field ϕ ( x ) .

Neumann condition in the Schrödinger-Maxwell system

We study a system of (nonlinear) Schrodinger and Maxwell equation in a bounded domain, with a Dirichelet boundary condition for the wave function

Born–Infeld type equations for electrostatic fields

\psi

Remarks on topological solitons

and a nonhomogeneous Neumann datum for the electric potential

Periodic solutions with prescribed energy for singular conservative systems involving strong forces

\phi

Asymptotically linear elliptic problems at resonance

. Under a suitable compatibility condition, we establish the existence of infinitely many static solutions

Existence of a time-like periodic trajectory for a time-dependent Lorentz metric

\psi=u(x)

Stability properties for solitary waves in 3 space dimensions

in equilibrium with a purely electrostatic field

Multiple solutions for elliptic equations at resonance

{\bold E}=-\nabla\phi