Multiple symmetric positive solutions for discrete Lidstone boundary valueproblems

For the 2mth order difference equation, (-1)(m)Delta (2m)y(t - m) = f(y(t)) , t is an element of {1, 2,..., T + 1}, satisfying the Lidstone boundary co nditions, Delta (2i)y(-m + 1) = 0, 0 less than or equal to i less than or e qual to m - 1, and Delta (2j)y(T + m + 1 - 2j) = 0, 0 less than or equal to j less than or equal to m - 1, where f : R --> [0, infinity), growth condt ions are imposed on f which yield the existence of at least three symmetric positive solutions.