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 Delta(n)Y+F(k,y Delta y,...,Delta(n-2)y)=G(k,y,Delta(n-1)y), n-1 less than or equal to k less than or equal to N, Delta(i)y(0)=0, 0 less than or equal to i less than or equal to n-2, Delta(p)y(N+n-p)=0, where n greater than or equal to 2 and 0 less than or equal to p less than or equal to 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.