Neumann condition in the Schrödinger-Maxwell system
Keywords
Schrödinger equation, stationary solutions, electrostatic field, variational methods, eigenvalue problemAbstract
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 $\omega$.Downloads
Published
2007-06-01
How to Cite
1.
PISANI, Lorenzo and SICILIANO, Gaetano. Neumann condition in the Schrödinger-Maxwell system. Topological Methods in Nonlinear Analysis. Online. 1 June 2007. Vol. 29, no. 2, pp. 251 - 264. [Accessed 29 March 2024].
Issue
Section
Articles
Stats
Number of views and downloads: 0
Number of citations: 0