  Chapman's model for ozone concentration is studied. In this nonlinear model,
the photodissociation coefficients for $O_{2}$ and $O_{3}$ are time-depending
due to earth-rotation. From the Kapitsa's method, valid in the high frequency
limit, we find the criterion for the existence of equilibrium solutions. These
solutions are depending on the frequency, and require a rotation period $T$
which satisfies $T<T_{1}$ or $T>T_{2}$. Where the critical periods $T_{1}$ and
$T_{2}$, with $T_{2}>T_{1}$, are a function of the parameters of the system
(reaction rates and photodissociation coefficients). Conjectures respect to the
retardation of the earth's rotation, due to friction, suggest that the
criterion was not even verified in the atmospheric past.
