In this paper we show that, under suitable conditions on f and K, the inequalities -lambda + theta integral(0)(infinity) epsilon(lambda s) K(s) ds > 0 for all lambda 0 and -lambda(2) + theta integral(0)(infinity) e(lambda s) K(s) ds > 0 for all lambda > 0 imply the integro-differential inequalities y'(t) + integral(0)(t) K(t - s)f(y(s)) ds less than or equal to 0 on (T, infinity) and y ''(t) - integral(0)(t) K(t - s)f(y)s)) ds greater than or equal to 0 on [T, infinity) have no positive solution, respectively, where f(y)ly greater than or equal to theta > 0 in some interval (0, y(0)). We also point out that the function f cannot be a superlinear function, that is, f(y) not equal y beta for beta is an element of (1, infinity).
