  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 w = -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.
