We study a system of (nonlinear) Schroedinger and Maxwell equation in a bounded domain, with a Dirichelet boundary condition for the wave function ψ and a nonhomogeneous Neumann datum for the electric potential φ. Under a suitable compatibility condition, we establish the existence of infinitely many static solutions ψ = u(x) in equilibrium with a purely electrostatic field E = −∇φ. Due to the Neumann condition, the same electric field is in equilibrium with stationary solutions ψ = u(x)exp(−iωt) of arbitrary frequency ω.
Neumann Condition in the Schroedinger-Maxwell system
PISANI, Lorenzo;SICILIANO G.
2007-01-01
Abstract
We study a system of (nonlinear) Schroedinger and Maxwell equation in a bounded domain, with a Dirichelet boundary condition for the wave function ψ and a nonhomogeneous Neumann datum for the electric potential φ. Under a suitable compatibility condition, we establish the existence of infinitely many static solutions ψ = u(x) in equilibrium with a purely electrostatic field E = −∇φ. Due to the Neumann condition, the same electric field is in equilibrium with stationary solutions ψ = u(x)exp(−iωt) of arbitrary frequency ω.File in questo prodotto:
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