Stationary solutions of the Schrödinger-Newton model - An ODE approach

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dc.creatorChoquard, Philippe
dc.creatorStubbe, Joachim
dc.creatorVuffray, Marc
dc.date2007-12-19
dc.date2008-02-13
dc.date.accessioned2026-07-07T09:20:08Z
dc.date.available2026-07-07T09:20:08Z
dc.descriptionWe prove the existence and uniqueness of stationary spherically symmetric positive solutions for the Schrödinger-Newton model in any space dimension $d$. Our result is based on an analysis of the corresponding system of second order differential equations. It turns out that $d=6$ is critical for the existence of finite energy solutions and the equations for positive spherically symmetric solutions reduce to a Lane-Emden equation for all $d\geq 6$. Our result implies in particular the existence of stationary solutions for two-dimensional self-gravitating particles and closes the gap between the variational proofs in $d=1$ and $d=3$.
dc.identifierhttps://arxiv.org/abs/0712.3103
dc.identifierhttp://arxiv.org/abs/0712.3103
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/154628
dc.subjectMathematical Physics
dc.subject35Q55, 35Q40, 47J10
dc.titleStationary solutions of the Schrödinger-Newton model - An ODE approach
dc.typetext

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