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. (C) 1994 Academic Press, Inc.