Abstract
We consider boson star solutions in a D-dimensional, asymptotically anti-de Sitter spacetime and investigate the influence of the cosmological term on their properties. We find that for D>3 the boson star properties are close to those in four dimensions with a vanishing cosmological constant. A different behavior is noticed for the solutions in the three dimensional case. We establish also the non-existence of static, spherically symmetric black holes with a harmonically time-dependent complex scalar field in any dimension greater than two.
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