  In this work we study interacting electrons on square lattice in the presence
of strong Rashba spin-orbit interaction. The spin-orbit term forces the
time-reversal electron states to be paired in even Cooper channels. For
concreteness, we only consider the repulsive onsite Hubbard and
nearest-neighbor coulomb interactions, the so called extended Hubbard model. To
examine the superconducting instability we obtain the effective interaction
between electrons within the random phase approximation and treat the pairing
instabilities driven by charge and spin fluctuations and their combined
effects. We mapped out the phase diagram of the model in terms of interactions
and electron fillings, and found that while the $d_{xy}$ and $d_{x^2-y^2}$
symmetries are the most likely pairing symmetries driven by charge and spin
fluctuations, respectively, the strong effect of both fluctuations yields
higher angular momentum Cooper instability. The possibility of topological
superconductivity and triplet pairing is also discussed.
