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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)
This paper deals with the Klein-Gordon-Maxwell system in a bounded spatial domain. We study the existence of solutions having a specific form, namely standing waves in equilibrium with a purely electrostatic field. We prescribe Dirichlet boundary conditions on the matter field, and either Dirichlet or Neumann boundary conditions on the electric potential.
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)