Existence of triple solutions of discrete (n, p) boundary value problems

We consider the following boundary value problem: -Delta (n)y = F(k, y, Del tay,..., Delta (n-1)y), k is an element of Z[n - 1, 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 p is a fixed integer satisfyi ng 0 less than or equal to p less than or equal to n - 1. Using a fixed-poi nt theorem for operators on a cone, we shall yield the existence of at leas t three positive solutions. (C) 2001 Elsevier Science Ltd. All rights reser ved.