In this paper, a full-duplex unmanned aerial vehicle (UAV) base station is used to provide wireless communication to an area lacking a conventional terrestrial infrastructure, and its efficient deployment is investigated. More concretely, the UAV positioning and resource allocation problems are solved with the aim of minimizing the transmit power of the UAV, while serving users with their rate requirements and accounting for the backhaul limitation of the UAV. To this end, a complete solution for the optimal 3D position of the UAV, the bandwidth assignment and the transmit power distribution in the access and backhaul links is proposed that accounts for both the backhaul interference and the self-interference. When the UAV power budget is insufficient to fulfill rate requirements, NOMA pairing is conducted to enhance system performance. Simulation results show that, when using the proposed approach, both the achieved sum rate and the percentage of satisfied users are significantly increased, when compared to a strategy that uses separate frequency bands in the access and backhaul links, as well as to a previously proposed method.