Positive Solutions of Complementary Lidstone Boundary Value Problems

We consider the following complementary Lidstone boundary value problem (-1)(m) y((2m+1)) (l) = F(l, y(l), y'(l)), l is an element of [0, 1] y(0) = 0, y ((2k-1))(0) = y((2k-1))(1) = 0, 1 <= k <= m. The nonlinear term F depends on y' and this derivative dependence is seldom investigated in the literature. Using a variety of fixed point theorems, we establish the existence of one or more positive solutions for the boundary value problem. Examples are also included to illustrate the results obtained.