Stable Subharmonic Solutions in Periodic Reaction-Diffusion Equations

We construct an example of a T-periodic semilinear reaction-diffusion equation whose elliptic part is in divergence form for each t, and which admits stable periodic solutions of higher minimal period. Thus there is no generic convergence to T-periodic solutions. This is in sharp contrast to the autonomous case, where the existence of a Lyapunov function implies quasiconvergence for all bounded solutions.