  We study black hole solutions in the Einstein gravity with Gauss-Bonnet term,
the dilaton and a positive "cosmological constant" in various dimensions.
Physically meaningful black holes with a positive cosmological term are
obtained only for those in static spacetime with $(D-2)$-dimensional hyperbolic
space of negative curvature and $D>4$. We construct such black hole solutions
of various masses numerically in $D=5,6$ and 10 dimensional spacetime and
discuss their properties. In spite of the positive cosmological constant the
spacetime approach anti-de Sitter spacetime asymptotically. The black hole
solutions exist for a certain range of the horizon radius, i.e., there are
lower and upper bounds for the size of black holes. We also argue that it is
quite plausible that there is no black hole solution for hyperbolic space in
the case of no cosmological constant.
