Inflationary Brans-Dicke Quantum Universe II: Particular evolutions and   stability analysis
  We made an analysis of the equations of motion which are obtained from the one - loop effective action for Brans-Dicke gravity with N dilaton - coupled massless fermions in a time-dependent conformally flat background. Various particular solutions, including the well-known stationary one, of the corresponding set of first-order differential equations are given. Some of these solutions describe an expanding time-dependent Universe with increasing, constant or also decreasing dilaton. This is illustrated by a numerical analysis. For the nonstationary solutions a stability analysis is given. 
B. Geyer, V. F. Kovalev