Multiple solutions of difference and partial difference equations with Lidstone conditions

This paper considers the following boundary value problem: (-1)(m)Delta(2m)y = F(k, y, Delta u,..., Delta(2m-1)y), m greater than or e qual to 1, 0 less than or equal to k less than or equal to N, Delta(2i)y(0) - Delta(2i)y(N + 2m - 2i) = 0, 0 less than or equal to i less than or equa l to m-1. We offer criteria for the existence of double and triple positive solutions of the boundary value problem. In addition, for special cases upper and lo wer bounds are established for these positive solutions. As an application, we also investigate the existence of radial solutions of certain partial d ifference equation. Several examples are included to dwell upon the importa nce of the results obtained. (C) 2000 Elsevier Science Ltd. All rights rese rved.