  In this work we consider a current carrying molecular junction with both
electron-phonon and electron-electron interactions taken into account. After
performing Lang-Firsov transformation and considering Markov approximations in
accordance to weak coupling to the electronic leads, we obtain the master
equation governing the time evolution of the reduced density matrix of the
junction. The steady state of the density matrix can be used to obtain I-V
characteristic of the junction in several regimes of strengths of the
interactions. Our results indicate that the system can show negative
differential conductance (that is, the current decreases by increasing the
applied bias voltage) in some regimes as an interplay between the
electron-phonon and Coulomb interactions.
