Bubbles are formed in a fluid by inflating a liquid film with a gas in which the pressure $\hat{\pi}(\nu)$ is a strictly decreasing function of the specific volume, unbounded as $\nu \rightarrow 0^{+}$. We show that, if $\hat{\pi}(\nu)$ grows as fast or faster than $\nu^{-2/3}$ as $\nu \rightarrow 0^{+}$, 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 $\hat{\pi}(\nu)$ grows as slowly or slower than $\nu^{-1/3}$ as $\nu \rightarrow 0^{+}$, then any such bubble has no equilibrium configuration, when the amount of gas within it is too small.