  We prove that if $K$ is a complete algebraically closed non-archimedian
valuation field of positive characteristic and $f$ is an endomorphism of
$\mathbb{P}_{K}^{N}$ which is totally inseparable and behaves as the Frobenius
on the special fiber, then $f$ satisfies the dynamical Mordell-Lang (DML)
property. We also discuss some corollaries and generalizations.
