A Mathematical Model for the Spectrum of a Two-Dimensional Schrödinger Equation with Magnetic Field under Dirichlet Boundary Conditions

2000 ◽  
Vol 61 (2) ◽  
pp. 129-132
Author(s):  
Miriam Manoel ◽  
José Camilo Barbosa
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Schrodinger Equation ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Two Dimensional

Multiple Solutions for Perturbed Elliptic Equations in Unbounded Domains

2003 ◽  
Vol 3 (1) ◽  
pp. 1-23 ◽  
Author(s):  
A. Salvatore
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Perturbation Method ◽  
Elliptic Equations ◽  
Multiple Solutions ◽  
Schrodinger Equation ◽  
Dirichlet Boundary ◽  
Unbounded Domains ◽  
Dirichlet Boundary Conditions

AbstractWe look for solutions of a nonlinear perturbed Schrödinger equation with nonhomogeneous Dirichlet boundary conditions. By using a perturbation method introduced by Bolle, we prove the existence of multiple solutions in spite of the lack of the symmetry of the problem.

scholarly journals On the cubic NLS on 3D compact domains

2013 ◽  
Vol 13 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Fabrice Planchon
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Bounded Domain ◽  
Schrodinger Equation ◽  
Dirichlet Boundary ◽  
Smooth Boundary ◽  
Dirichlet Boundary Conditions ◽  
Well Posedness ◽  
Bounded Domains ◽  
Bilinear Estimates

AbstractWe prove bilinear estimates for the Schrödinger equation on 3D domains, with Dirichlet boundary conditions. On non-trapping domains, they match the ${ \mathbb{R} }^{3} $ case, while on bounded domains they match the generic boundaryless manifold case. We obtain, as an application, global well-posedness for the defocusing cubic NLS for data in ${ H}_{0}^{s} (\Omega )$, $1\lt s\leq 3$, with $\Omega $ any bounded domain with smooth boundary.

Large Time Behavior of Solutions to One Nonlinear Integro-Differential Equation

2008 ◽  
Vol 15 (3) ◽  
pp. 531-539
Author(s):  
Temur Jangveladze ◽  
Zurab Kiguradze
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Boundary Conditions ◽  
Large Time ◽  
Dirichlet Boundary ◽  
Large Time Behavior ◽  
Dirichlet Boundary Conditions ◽  
Time Behavior ◽  
Integro Differential Equation ◽  
Homogeneous Data

Abstract Large time behavior of solutions to the nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance is studied. The rate of convergence is given, too. Dirichlet boundary conditions with homogeneous data are considered.

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