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We predict the existence of an energy barrier for collapse in a system of twotunnel-coupled repulsive and attractive quasi two-dimensional condensatestrapped in a double-well potential. The ground state in such a system can havea lower energy than that of the collapsing state. We find such ground statesnumerically and analytically determine the domain of their existence, they havea much larger share of atoms confined in the repulsive condensate. The energybarrier for collapse is due to the fact that the energy of the system increasesif atoms tunnel from the repulsive condensate to the attractive one.Comment: Latex, 14 pages, 4 figure

Energy barrier for collapse in a pair of tunnel-coupled condensates with scattering lengths of opposite signs