Dilaton black holes in the de Sitter or anti–de Sitter universe

Poletti and Wiltshire have shown that, with the exception of a pure cosmological constant, the solution of a dilaton black hole in the background of de Sitter or anti--de Sitter universe, does not exist in the presence of one Liouville-type dilaton potential. In this work we obtain the dilaton black-hole solutions in the background of the de Sitter or anti--de Sitter universe, with the combination of three Liouville-type dilaton potentials.