The asymptotic  behavior of most bounded  solutions of such equations is   governed by stable periodic solutions.    We address the question whether a stable periodic  solution    can be subharmonic, that  is, whether its  minimal period   can  be larger  than the  period  of the equation.   While there are no such  solutions on a  convex domain, we show  that on some nonconvex   domains stable subharmonic solutions do occur (if the nonlinearity is chosen suitably).