Serverless computing is a promising approach for edge computing since its inherent features, e.g., lightweight virtualization, rapid scalability, and economic efficiency. However, previous studies have not studied well the issues of significant cold start latency and highly dynamic workloads in serverless function scheduling, which are exacerbated at the resource-limited network edge. In this paper, we formulate the Serverless Function Scheduling (SFS) problem for resource-limited edge computing, aiming to minimize the average response time. To efficiently solve this intractable scheduling problem, we first consider a simplified offline form of the problem and design a polynomial-time optimal scheduling algorithm based on each function's weight. Furthermore, we propose an Enhanced Shortest Function First (ESFF) algorithm, in which the function weight represents the scheduling urgency. To avoid frequent cold starts, ESFF selectively decides the initialization of new function instances when receiving requests. To deal with dynamic workloads, ESFF judiciously replaces serverless functions based on the function weight at the completion time of requests. Extensive simulations based on real-world serverless request traces are conducted, and the results show that ESFF consistently and substantially outperforms existing baselines under different settings.