  For units $\delta$ and $\alpha$ in $\F_{p^m}$, the structure of
$(\delta+\alpha u^2)$-constacyclic codes of length $p^k$ over
$\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}+u^2\mathbb{F}_{p^m}$ is studied and
self-dual $(\delta+\alpha u^2)$-constacyclic codes are analyzed.
