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 ${\mathbf{E}}=-\nabla\phi$. 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 $\omega$.
Citation
Lorenzo Pisani. Gaetano Siciliano. "Neumann condition in the Schrödinger-Maxwell system." Topol. Methods Nonlinear Anal. 29 (2) 251 - 264, 2007.
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