Zhan Kuan GUO,Jiong SUN
In the paper, we considered a class of ordinary differential expressions as following:=0(-1)kDkeanxDk and =0(-1)kakDkenxDk, proved that their indexes are {n, n + 2,..., 2n- l} or {n, n + 2,..., 2n-2} or a subset of them, and gave some examples of positive coefficient ordinary differential operators with middle deficiency indexes. These examples show that positive coefficient ordinary differential operators needn't to be all limit-point, this is, we give a negative answer to Everitt's conjecture in another way.