  We consider Brans-Dicke theory with a self-interacting potential in Einstein
conformal frame. We introduce a class of solutions in which an accelerating
expansion is possible in a spatially flat universe for positive and large
values of the Brans-Dicke parameter consistent with local gravity experiments.
In this Einstein frame formulation, the theory appears as an interacting
quintessence model in which the interaction term is given by the conformal
transformation. In such an interacting model, we shall show that the solutions
lead simultaneously to a constant ratio of energy densities of matter and the
scalar field.
