In this paper, we show the existence of
stable and unstable
$T-$periodic solutions for a semilinear parabolic equation
$\frac{\partial u}{\partial t} - \Delta u =
g(x,u) + h( t, x ),\quad \text{in} \quad (0,T) \times \Omega$
$u=0 ,\quad \text{on}\quad (0,T) \times \partial \Omega$
$u(0) = u(T),\quad \text{in} \quad \overline \Omega$
where $\Omega \subset R^N$ is a bounded domain with a smooth boundary,
$g:\overline{\Omega} \times R \rightarrow R$ is a continuous function such that
$g(x,\cdot )$ has a superlinear growth for each $x \in \overline{\Omega} $ and
$h:(0,T) \times \Omega \to R$ is a continuous function.
{{journal.titleEn}} 
DownLoad: