ar X iv : 0 71 2 . 31 03 v 1 [ m at h - ph ] 1 9 D ec 2 00 7 STATIONARY SOLUTIONS OF THE SCHRÖDINGER - NEWTON MODEL - AN ODE APPROACH
نویسندگان
چکیده
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 a careful 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 ≥ 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.
منابع مشابه
ar X iv : 0 70 7 . 03 46 v 1 [ m at h - ph ] 3 J ul 2 00 7 THE ONE - DIMENSIONAL SCHRÖDINGER - NEWTON EQUATIONS
We prove an existence and uniqueness result for ground states of one-dimensional Schrödinger-Newton equations.
متن کاملar X iv : 0 71 2 . 31 69 v 1 [ m at h . A P ] 1 9 D ec 2 00 7 The parabolic - parabolic Keller - Segel model in R 2 ∗
This paper is devoted mainly to the global existence problem for the two-dimensional parabolicparabolic Keller-Segel in the full space. We derive a critical mass threshold below which global existence is ensured. Using carefully energy methods and ad hoc functional inequalities we improve and extend previous results in this direction. The given threshold is supposed to be the optimal criterion,...
متن کاملar X iv : m at h - ph / 0 21 20 57 v 1 1 9 D ec 2 00 2 RANDOM SCHRÖDINGER OPERATORS ON MANIFOLDS
We consider a random family of Schrödinger operators on a cover X of a compact Riemannian manifold M = X/Γ. We present several results on their spectral theory, in particular almost sure constancy of the spectral components and existence and non-randomness of an integrated density of states. We also sketch a groupoid based general framework which allows to treat basic features of random operato...
متن کاملar X iv : h ep - t h / 03 12 24 4 v 1 1 9 D ec 2 00 3 FIAN / TD / 07 – 03 On Sp ( 2 M ) Invariant Green Functions
Explicit form of two-point and three-point Sp (2M) invariant Green functions is found.
متن کاملar X iv : h ep - t h / 03 12 06 2 v 2 7 D ec 2 00 3 More Membrane Matrix Model Solutions , – and Minimal Surfaces in S 7 Joakim
New solutions to the classical equations of motion of a bosonic matrix-membrane are given. Their continuum limit defines 3-manifolds (in Minkowski space) whose mean curvature vanishes. Part of the construction are minimal surfaces in S, and their discrete analogues. Some time ago [1], solutions of the bosonic matrix-model equations, .. Xi = − d ∑ j=1 [ [ Xi, Xj ] , Xj ]
متن کامل