  The Lagrangian of a hypergraph has been a useful tool in hypergraph extremal
problems. In most applications, we need an upper bound for the Lagrangian of a
hypergraph. Frankl and Furedi in \cite{FF} conjectured that the $r$-graph with
$m$ edges formed by taking the first $m$ sets in the colex ordering of
${\mathbb N}^{(r)}$ has the largest Lagrangian of all $r$-graphs with $m$
edges. In this paper, we give some partial results for this conjecture.
