  We consider a generalized Brans-Dicke model in which the scalar field has a
self-interacting potential function. The scalar field is also allowed to couple
non-minimally with the matter part. We assume that it has a chameleon behavior
in the sense that it acquires a density-dependent effective mass. We consider
two different types of matter systems which couple with the chameleon, dust and
vacuum. In the first case, we find a set of exact solutions when the potential
has an exponential form. In the second case, we find a power-law exact solution
for the scale factor. In this case, we will show that the vacuum density decays
during expansion due to coupling with the chameleon.
