In this paper, we study resource management and allocation for Energy Harvesting Cognitive Radio Sensor Networks (EHCRSNs). In these networks, energy harvesting supplies the network with a continual source of energy to facilitate self-sustainability of the power-limited sensors. Furthermore, cognitive radio enables access to the underutilized licensed spectrum to mitigate the spectrum-scarcity problem in the unlicensed band. We develop an aggregate network utility optimization framework for the design of an online energy management, spectrum management and resource allocation algorithm based on Lyapunov optimization. The framework captures three stochastic processes: energy harvesting dynamics, inaccuracy of channel occupancy information, and channel fading. However, a priori knowledge of any of these processes statistics is not required. Based on the framework, we propose an online algorithm to achieve two major goals: first, balancing sensors