  We predict the existence of an energy barrier for collapse in a system of two
tunnel-coupled repulsive and attractive quasi two-dimensional condensates
trapped in a double-well potential. The ground state in such a system can have
a lower energy than that of the collapsing state. We find such ground states
numerically and analytically determine the domain of their existence, they have
a much larger share of atoms confined in the repulsive condensate. The energy
barrier for collapse is due to the fact that the energy of the system increases
if atoms tunnel from the repulsive condensate to the attractive one.
