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- W3100783361 abstract "We study the qualitative properties of ground states of the time-independent magnetic semilinear Schrödinger equation − ( ∇ + i A ) 2 u + u = | u | p − 2 u in R N where the magnetic potential A induces a constant magnetic field. When the latter magnetic field is small enough, we show that the ground state solution is unique up to magnetic translations and rotations in the complex phase space, that ground state solutions share the rotational invariance of the magnetic field and that the presence of a magnetic field induces a Gaussian decay. In this small magnetic field régime, the corresponding ground-energy is a convex differentiable function of the magnetic field. Nous étudions les propriétés qualitatives des états fondamentaux de l'équation de Schrödinger stationnaire − ( ∇ + i A ) 2 u + u = | u | p − 2 u in R N où le potentiel magnétique A induit un champ magnétique constant. Lorsque ce champ magnétique est suffisamment petit, nous montrons que l'état fondamental est unique à translation magnétique ou rotation dans l'espace complexe des phases près, qu'il hérite des invariances par rotation du champ magnétique et que la présence du champ magnétique induit une décroissance gaussienne. Dans le régime de petit champ magnétique, l'énergie fondamentale est une fonction convexe différentiable du champ magnétique." @default.
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- W3100783361 date "2019-04-01" @default.
- W3100783361 modified "2023-09-29" @default.
- W3100783361 title "Properties of ground states of nonlinear Schrödinger equations under a weak constant magnetic field" @default.
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- W3100783361 doi "https://doi.org/10.1016/j.matpur.2018.05.007" @default.
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