We investigate cosmological solutions of Brans-Dicke theory with both the vacuum energy density and the gravitational constant decaying linearly with the Hubble parameter .
A particular class of them , with constant deceleration factor , sheds light on the cosmological constant problems , leading to a presently small vacuum term , and to a constant ratio between the vacuum and matter energy densities .
By fixing the only free parameter of these solutions , we obtain cosmological parameters in accordance with observations of both the relative matter density and the universe age .
In addition , we have three other solutions , with Brans-Dicke parameter \omega = -1 and negative cosmological term , two of them with a future singularity of big-rip type .
Although interesting from the theoretical point of view , two of them are not in agreement with the observed universe .
The third one leads , in the limit of large times , to a constant relative matter density , being also a possible solution to the cosmic coincidence problem .