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In cognitive radio networks, the arrival of Primary Users (PUs) may force Secondary Users (SUs) to terminate their ongoing sessions or degrade their Quality of Service (QoS) level. Given the time-varying spectrum availability, an immediate challenge arising is to support the QoS of SUs under spectrum mobility. In this paper, we propose an optimal decision-making framework for joint admission control, eviction control and bandwidth adaptation in cognitive radio networks. The problem is formulated as a Semi-Markov Decision Process (SMDP) and the optimal decision for each system state is derived to maximize the long-term network revenue as a function of the spectrum utilization, the SU blocking probability and the bandwidth adaptation cost under the SU dropping probability constraint. It is shown that the derived optimal strategy outperforms the threshold-based channel reservation schemes with/without bandwidth adaptation. And among the schemes with bandwidth adaptation, more performance improvement can be achieved by the proposed one when the bandwidth adaptation cost is taken into account.