Sunflowers and $L$-intersecting families

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