Double solutions of boundary value problems for 2m(th)-order differential equations and difference equations
A double fixed-point theorem is applied to obtain the existence of at least two positive solutions for the boundary value problem, (-1)(m)y((2m)) (t) = f (y(t)), t is an element of [0, 1], y((2i)) (0) = y((2i+1)) (1) = 0, 0 less than or equal to i less than or equal to m - 1. It is later applied to obtain the existence of at least two positive solutions for the analogous discrete boundary value problem, (-1)(m)Delta(2m)u(k) = g(u(k)), k is an element of {0,...,N}, Delta(2i)u(0) = Delta(2i+1)u(N + 1) = 0, 0 less than or equal to i less than or equal to m - 1. (C) 2003 Elsevier Science Ltd. All rights reserved.
boundary value problem green's function multiple solutions