In recent years, mobile edge computing (MEC) has been proposed as a promising technique to alleviate the challenges faced by delay and computation-intensive applications. However, users in remote and mountainous areas continue to face difficulties obtaining reliable computation services. To overcome this obstacle, unmanned aerial vehicles (UAVs) equipped with MEC servers have emerged as a popular solution. In such a multi-UAV network, the coverage areas of the UAVs might overlap, which would result in resource wastage and interference. To address this issue, we investigate a collaborative UAV-assisted MEC system for both aerial users (AUs) and ground users (GUs) in this work. Specifically, each user is covered by multiple UAV servers, and the resources of UAVs are dynamic over time. The main objective of this work is to reduce the average delay and improve the service success rate by jointly designing the UAV server-user association, bandwidth, and computing resource allocation strategy. To address the non-convex optimization problem mentioned above, we formulate a multi-agent extension of Markov decision processes (MDPs) for the system and design a cooperative Multi-Agent Twin Delayed Deep Deterministic Policy Gradient (MATD3) approach for each UAV server to make decisions using a centralized training approach with distributed execution. Simulation results validate that the proposed approach can achieve a superior success service rate with a lower delay compared with baselines.