In this paper, we investigate the resource allocation design for multicarrier (MC) systems employing a solar powered unmanned aerial vehicle (UAV) for providing communication services to multiple downlink users. We study the joint design of the three-dimensional positioning of the UAV and the power and subcarrier allocation for maximization of the system sum throughput. The algorithm design is formulated as a mixed-integer non-convex optimization problem, which requires a prohibitive computational complexity for obtaining the globally optimal solution. Therefore, a low-complexity suboptimal iterative solution based on successive convex approximation is proposed. Simulation results confirm that the proposed suboptimal algorithm achieves a substantially higher system sum throughput compared to several baseline schemes.