Title: AN EXISTENCE AND UNIQUENESS THEOREM FOR ORDINARY DIFFERENTIAL EQUATIONS IN ORDERED BANACH SPACES
Abstract: We prove that the initial value problem x'(t) = g(t,x(t)) + h(t, x(t)), t € [0, T], x(0) = a, is uniquely solvable in certain partially ordered Banach spaces if, with respect to x, g is one-sided Lipschitz continuous, h is montonic decreasing and g + h is quasimonotonic increasing.