Triple positive solutions and dependence on higher order derivatives

In this paper, we consider the Lidstone boundary value problem, y((2m))(t) = f(y(t),...,y((2j))(t)... y((2(m-1)))(t)), 0 less than or equal to t less than or equal to 1, y((2i))(0) = 0 = y((2i))(1), 0 less than or equal to i less than or equal to m - 1, where (-1)(m) f> 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. (C) 1999 Academic Press.