Triple solutions of complementary Lidstone boundary value problems via fixed point theorems

We consider the following complementary Lidstone boundary value problem: (-1)(m)y((2m+1))(t) = F (t,y(t), y'(t)). t is an element of [0, 1], y(0) = 0, y((2k-1))(0) = y((2k-1))(1) = 0, 1 <= k <= m. By using fixed point theorems of Leggett-Williams and Avery, we offer several criteria for the existence of three positive solutions of the boundary value problem. Examples are also included to illustrate the results obtained. We note that the nonlinear term F depends on y' and this derivative dependence is seldom investigated in the literature and a new technique is required to tackle the problem.