The higher-order Picone identity and comparison of half-linear differential equations of even order

An identity of the Picone type for higher-order half-linear ordinary differential operators of the form and where p_j and P_j, j=0,…,n, are continuous functions defined on a,b] and , is derived and then the Sturmian comparison theory for the corresponding 2nth-order equations l_αx]=0 and L_αy]=0 based on this identity is developed.