Unmanned aerial vehicles (UAVs) can enhance the overall performance of terrestrial communication systems due to their high possibility of the line of sight (LoS) links and on-demand deployments. The advantages of the UAV position optimization now attract attentions from researchers to study the cooperation among static UAV relays. In this paper, we study a relaying system, where multiple UAVs establish a cooperative UAV relay network to help some transmitters (Txs) communicate with their corresponding receivers (Rxs) by employing orthogonal frequency division multiple access (OFDMA). We maximize the paired Tx-Rxs' minimum rate through solving a non-convex, information causality constraints involved problem by optimizing the UAV relays' locations, nodes' powers, and bandwidth allocations together. An iterative algorithm is proposed by using block coordinate descent (BCD) and successive convex approximation (SCA) methods. Moreover, we also propose a new position initialization method, discuss some special cases of our problem to show some insights for future works, and prove the convergence of our algorithm. Simulations show the effectiveness of our proposed algorithm, some interesting trade-offs about the optimized UAVs' locations, and the influence of available resources.