We consider the model of a false vacuum bubble with a thin wall where the surface energy density is composed of two different components, "domain-wall" type and "dust" type, with opposite signs. We find stably oscillating solutions, which we call "breathing bubbles". By decay to a lower mass state, such a breathing bubble could become either i) a child universe or ii) a bubble that "eats up" the original universe, depending on the sign of the surface energy of the "domain-wall" component. We

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... o discuss the effect of the finite-thickness corrections to the thin-wall approximation and possible origins of the energy contents of our model.