  The competition between parametric resonance (PR) and dissipation is studied
in the damped Kronig-Penney model, with time-dependent dissipation rate
gamma(t). In the classical case, it is shown that dissipation leaves just a
finite number of PR-bands at most, suppressing those at higher frequencies. An
analysis of the Lewis-Reisenfeld invariant I(q,p,rho) is performed, showing
that, in the PR regime, the auxiliary function rho(t) can be chosen bounded or
unbounded, depending on the initial conditions.
