Triple Positive Solutions and Dependence on Higher Order Derivatives

In this paper, we consider the Lidstone boundary value problem, y 2m. t.s f y t., . . . ,y 2 j. t., . . .y 2 my1.. t.., 0FtF1, y 2 i. 0.s0sy 2 i. 1., 0FiFmy 1, where y1.mf)0. Growth conditions are imposed on f and inequalities involving an associated Green’s function are employed which enable us to apply the Leggett]Williams Fixed Point Theorem to cones in ordered Banach spaces. This in turn yields the existence of at least three positive symmetric concave solutions. The emphasis here is that f depends on higher order derivatives