Double positive solutions of (n,p) boundary value problems for higher order difference equations

We shall provide existence criteria for double positive solutions of the (n,p) boundary value problem δ n y+F(k,y,δy,…,δ n-2 y)=G(k,y,δy…,δ n−1 y) , n−1⩽k⩽N , δ i y(0)=0 , 0⩽i⩽n−2 , δ p y(N+n−p)=0 , where n ≥ 2 and 0 ≤ p ≤ n − 1 is fixed. Upper and lower bounds for the two positive solutions are also established for a particular boundary value problem when n = 2. Several examples are included to dwell upon the importance of the results obtained.