Stability and stabilization of unstable condensates

It is possible to condense a macroscopic number of bosons into a single mode. Adding interactions the question arises whether the condensate is stable. For repulsive interaction the answer is positive with regard to the ground-state, but what about a condensation in an excited mode? We discuss some results that have been obtained for a 2-mode bosonic Josephson junction, and for a 3-mode minimal-model of a superfluid circuit. Additionally we mention the possibility to stabilize an unstable condensate by introducing periodic or noisy driving into the system: this is due to the Kapitza and the Zeno effects.