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Green energy is emerging as a promising alternative energy source to power network devices in next-generation wireless networks. Different from traditional energy, green energy is replenished from nature, e.g., solar and wind, and is highly dependent on the capacities and locations of the electronic devices. As such, the fundamental design criterion in the network deployment and management is shifted from energy efficiency to energy sustainability due to the sustainable nature of green energy. In this paper, we study the network resource management issues in next-generation wireless networks with sustainable energy supply. Our objective is to deploy the minimal number of green RNs, i.e., RNs powered by green energy, and optimize resource allocation to ensure full network connectivity and users' Quality of Service (QoS) requirements can be fulfilled with the harvested energy based on the cost threshold. To this end, the RN placement and sub-carrier allocation (RNP-SA) issues are jointly formulated into a mixed integer non-linear programming problem. Two low-complexity heuristic algorithms, namely RNP-SA with top-down/bottom-up algorithms (RNP-SA-t/b), are presented to solve the non-linear programming problem in different network scenarios. Extensive simulations show that the proposed algorithms provide simple yet efficient solutions and offer important guidelines on network deployment and resource management in a green radio network with sustainable energy sources.