This paper addresses the joint task offloading and resource scheduling problem in Low Earth Orbit (LEO) satellite edge computing networks. The proposed network comprises a number of source low earth orbit (SLEO) satellites attempting to transmit their data flows to the designated ground stations (GSs). To address the long-term cost minimization problem in refeq:pro, a Dijkstra-based strategy is proposed for the transmission scheduling problem, while a deep learning method using DQN is adopted for dynamic task scheduling. Simulation results show significant improvements in average system cost, queue length, energy consumption, and task completion rate compared to baseline strategies.