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This paper investigates a multiple unmanned aerial vehicle (multi-UAV) assisted backscatter communication network (BCN), where multiple UAVs are employed to transmit RF carriers to as well as collect data from multiple backscatter sensor nodes (BSNs) deployed on the ground. We formulate an optimization problem to maximize the max-min rate of the BCN by jointly optimizing three blocks of variables, i.e., the UAVs' trajectories, the UAVs' transmission power and the BSNs' scheduling. The BSNs' sequential energy constraints are innovatively considered in our work. However, the formulated optimization problem is difficult to be solved due to its non-convexity and combinatorial nature. To this end, we use the block coordinate descent (BCD) method and successive convex approximation (SCA) technique. Numerical results show the impact of the BSNs' sequential energy constraint on the designed UAV trajectories and verify the gain of the proposed design in the max-min rate as compared to a benchmark scheme with UAV trajectory not optimized.