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 δny+F(k,y,δy,…,δn-2y)=G(k,y,δy…,δn−1y), n−1 k N, δiy(0)=0, 0 i n−2, δpy(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.