  Let $f(k,r,s)$ stand for the least number so that if $\cal F$ is an arbitrary
$k$-uniform, $L$-intersecting set system, where $|L|=s$, and $\cal F$ has more
than $f(k,r,s)$ elements, then $\cal F$ contains a sunflower with $r$ petals.
We give an upper bound for $f(k,3,s)$. Let $g(k,r,\ell)$ be the least number so
that any $k$-uniform, $\ell$-intersecting set system of more than $g(k,r,\ell)$
sets contains a sunflower with $r$ petals. We give also an upper bound for
$g(k,r,\ell)$.
