Bubbles are formed in a fluid by inflating a liquid film with a gas in which the pressure $\widehat{\pi }(\nu )$ is a strictly decreasing function of the specific volume, unbounded as $\nu \to 0^{+}$. We show that, if $\widehat{\pi }(\nu )$ grows as fast or faster than ${\nu }^{-2/3}$ as $\nu \to 0^{+}$, then there is at least one stable equilibrium configuration of any such bubble, no matter how much gas has been used to inflate it. On the other hand, if $\widehat{\pi }(\nu )$ grows as slowly or slower than ${\nu }^{-1/3}$ as $\nu \to 0^{+}$, then any such bubble has no equilibrium configuration, when the amount of gas within...