Neumann condition in the Schrödinger-Maxwell system
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Schrödinger equation, stationary solutions, electrostatic field, variational methods, eigenvalue problemAbstrakt
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 $\omega$.Pobrania
Opublikowane
2007-06-01
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1.
PISANI, Lorenzo & SICILIANO, Gaetano. Neumann condition in the Schrödinger-Maxwell system. Topological Methods in Nonlinear Analysis [online]. 1 czerwiec 2007, T. 29, nr 2, s. 251–264. [udostępniono 22.7.2024].
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