... ∞ is continuous and nonincreasing, and h may besingular at y 0. Throughout this paper, the topology on N will be the discrete topology.2. PreliminariesLet P be a normal c one of a Banach ... unique fixed point theorem for a class of mixed monotone op-erators, see 6, 14, 18. In virtue of the theorem, we consider the existence and uniqueness of solutions for the following singular higher-order ... 2007; Accepted 31 December 2007Recommended by Raul ManasevichBy mixed monotone method, the existence and uniqueness are established for singular higher-ordercontinuous and discrete boundary value...