  In this paper, we deal with limit cycle bifurcations near a double homoclinic
loop with a nilpotent saddle of order 2 by studying expansions of the first
order Melnikov functions near the loop and coefficients in these expansions.
More precisely, we prove that the perturbed system can have 11, 13, 14 or 16
limit cycles in a neighborhood of the loop under certain conditions. Finally,
we give an example to illustrate the effectiveness of our main results.
