Fine-tuning pre-trained large language models (LLM) in a distributed manner poses significant challenges on resource-constrained edge devices. To address this challenge, we propose FedsLLM, a novel framework that integrates split federated learning with parameter-efficient fine-tuning techniques. By leveraging model splitting and Low-Rank Adaptation (LoRA), FedsLLM reduces the computational burden on edge devices. Furthermore, the introduction of a federated server facilitates parallel training and enhances privacy. To accommodate heterogeneous communication conditions and diverse computational capabilities of edge devices, as well as the impact of LoRA rank selection on model convergence and training cost, we formulate a joint optimization problem. The formulated problem jointly optimizes subchannel allocation, power control, model splitting point selection, and LoRA rank configuration, all aimed at minimizing total training delay. An alternating optimization algorithm is developed to efficiently solve this problem and accelerate the training process. Simulation results demonstrate that the proposed FedsLLM framework achieves comparable model accuracy while significantly reducing client-side computational requirements. Furthermore, the proposed resource allocation scheme and adaptive LoRA rank selection strategy notably reduce the training latency compared to conventional approaches.