Distributed antenna systems have been proposed as a solution to supply the ever increasing capacity demands in next generation networks. This paper considers the power minimization problem in hybrid distributed antenna systems where antennas are supplied by various -low power and high power -energy sources. Antenna-specific power limits are considered and the problem is reformulated in this new hybrid context. The optimal power allocation problem is first formulated and solved in the orthogonal multiplexing scenario. Different resource allocations schemes based on this optimal power allocation are then proposed for the orthogonal and non-orthogonal multiplexing contexts. Simulation results illustrate the efficiency of the proposed algorithms and show the importance of non-orthogonal multiplexing in the reduction of the total transmission power, especially in hybrid antenna systems.