  We give the structure of $\lambda$-constacyclic codes of length $p^sm$ over
$R=\mathbb{F}_{p^r}+u \mathbb{F}_{p^r}+...+ u^{e-1}\mathbb{F}_{p^r}$ with
$\lambda \in \F_{p^r}^*$. We also give the structure of $\lambda$-constacyclic
codes of length $p^sm$ with $\lambda=\alpha_1+u\alpha_2+...+u^{e-1}
\alpha_{e-1}$, where $\alpha_1,\alpha_2 \neq 0$ and study the self-duality of
these codes.
