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- Lorenzo Pisani, Gaetano Siciliano
- Appl. Math. Lett.
- 2008

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.… (More)

In this paper we consider the stationary solutions of the Schrödinger-Poisson equation: iψt +∆ψ − (|x| ∗ |ψ|)ψ + |ψ|ψ = 0 in R. We are interested in the existence of standing waves, that is solutions of type ψ(x, t) = u(x)e−iωt, where ω ∈ R, with fixed L − norm. Then we are reduced to a constrained minimization problem. The main difficulty is the… (More)

In this paper we investigate the existence of positive solutions to the following Schrödinger-Poisson-Slater system

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 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 characterize the… (More)

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