Boson stars with negative cosmological constant

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 $D>4$ 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.