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2008 Stationary solutions of the Schrödinger-Newton model---an ODE approach
Philippe Choquard, Joachim Stubbe, Marc Vuffray
Differential Integral Equations 21(7-8): 665-679 (2008). DOI: 10.57262/die/1356038617


We 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 $d=3$.


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Philippe Choquard. Joachim Stubbe. Marc Vuffray. "Stationary solutions of the Schrödinger-Newton model---an ODE approach." Differential Integral Equations 21 (7-8) 665 - 679, 2008.


Published: 2008
First available in Project Euclid: 20 December 2012

zbMATH: 1224.35385
MathSciNet: MR2479686
Digital Object Identifier: 10.57262/die/1356038617

Primary: 35Q55
Secondary: 34A34 , 34L40 , 47J20

Rights: Copyright © 2008 Khayyam Publishing, Inc.


Vol.21 • No. 7-8 • 2008
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