  We revisit the stability of very massive nonrotating main-sequence stars at
solar metallicity, with the goal of understanding whether radial pulsations set
a physical upper limit to stellar mass. Models of up to 938 solar masses are
constructed with the Mesa code, and their linear stability in the fundamental
mode, assumed to be the most dangerous, is analysed with a fully nonadiabatic
method. Models above 100 MSun have extended tenuous atmospheres ("shelves")
that affect the stability of the fundamental. Even when positive, this growth
rate is small, in agreement with previous results. We argue that small growth
rates lead to saturation at small amplitudes that are not dangerous to the
star. A mechanism for saturation is demonstrated involving nonlinear parametric
coupling to short-wavelength g modes and the damping of the latter by radiative
diffusion. The shelves are subject to much more rapidly growing strange modes.
This also agrees with previous results but is extended here to higher masses.
The strange modes probably saturate via shocks rather than mode coupling but
have very small amplitudes in the core, where almost all of the stellar mass
resides. Although our stellar models are hydrostatic, the structure of their
outer parts suggests that optically thick winds, driven by some combination of
radiation pressure, transsonic convection, and strange modes, are more likely
than pulsation in the fundamental mode to limit the main-sequence lifetime.
