### Neumann condition in the Schrödinger-Maxwell system

DOI: http://dx.doi.org/10.12775/TMNA.2007.010

#### Abstract

We study a system of (nonlinear) Schrödinger and Maxwell equation in a

bounded domain, with a Dirichelet boundary condition for the wave function

$\psi$ and a nonhomogeneous Neumann datum for the electric potential $\phi$.

Under a suitable compatibility condition, we establish the existence of

infinitely many static solutions $\psi=u(x)$ in equilibrium with a

purely electrostatic field ${\bold E}=-\nabla\phi$. Due to the Neumann

condition, the same electric field is in equilibrium with stationary

solutions $\psi=e^{-i\omega t}u(x)$ of arbitrary frequency

$\omega$.

bounded domain, with a Dirichelet boundary condition for the wave function

$\psi$ and a nonhomogeneous Neumann datum for the electric potential $\phi$.

Under a suitable compatibility condition, we establish the existence of

infinitely many static solutions $\psi=u(x)$ in equilibrium with a

purely electrostatic field ${\bold E}=-\nabla\phi$. Due to the Neumann

condition, the same electric field is in equilibrium with stationary

solutions $\psi=e^{-i\omega t}u(x)$ of arbitrary frequency

$\omega$.

#### Keywords

Schrödinger equation; stationary solutions; electrostatic field; variational methods; eigenvalue problem

#### Full Text:

FULL TEXT### Refbacks

- There are currently no refbacks.