Gaetano Siciliano

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This paper is concerned with the Klein-Gordon-Maxwell system in a bounded spatial domain. We discuss the existence of standing waves ψ = u(x)e −iωt in equilibrium with a purely electrostatic field E = −∇φ(x). We assume an homogeneous Dirichlet boundary condition on u and an inhomogeneous Neumann boundary condition on φ. In the " linear " case we(More)
In this paper we investigate the existence of positive solutions to the following Schrödinger-Poisson-Slater system 8 < : −∆u + u + λφu = |u| p−2 u in Ω −∆φ = u 2 in Ω u = φ = 0 on ∂Ω where Ω is a bounded domain in R 3 , λ is a fixed positive parameter and p < 2 * = 2N N−2. We prove that if p is " near " the critical Sobolev exponent 2 * , then the number(More)
We study the existence of vortices of the Klein-Gordon-Maxwell equations in the two dimensional case. In particular we find sufficient conditions for the existence of vortices in the magneto-static case, i.e when the electric potential φ = 0. This result, due to the lack of suitable embedding theorems for the vector potential A is achieved with the help of(More)
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