With the rapid growth in the number of large language model (LLM) users, it is difficult for bandwidth-constrained cloud servers to simultaneously process massive LLM services in real-time. Recently, edge-cloud infrastructures have been used to improve the processing efficiency of large-scale LLM services. However, the diversity of task requirements and the dynamics of resources pose great challenges to inference scheduling, leading to the wastage of many resources. In this paper, we present PerLLM, a personalized inference scheduling framework with edge-cloud collaboration designed for diverse LLM services. For the complexity of multiple constraints and the decision-making process of edge-cloud collaboration, we integrate the upper confidence bound algorithm based on the constraint satisfaction mechanism in PerLLM. For diverse LLM services, PerLLM can optimize service scheduling and resource allocation solutions within the edge-cloud infrastructure to meet processing time requirements while minimizing energy costs. Experimental results from different model deployments show that PerLLM can effectively meet the processing time requirements of personalized services. Compared to other methods, PerLLM achieves 2.2x, 2.1x, and 1.6x throughput and reduces the energy cost by more than 50%.