POSITIVE SOLUTIONS OF INTEGRODIFFERENTIAL-INEQUALITIES

In this paper, we shall show that under suitable conditions on f and K , the inequalities -lambda(n) + integral(0)(infinity) e(lambda s) K(s) ds > 0, for all lambda > 0, (n=1,2,4) (I-n) imply that the integro-dif ferential inequalities (-1)(n+1)y((n))(t) + integral(0)(t) f(t-s,y(s)) ds less than or equal to 0, on [0,infinity), (n=1,2,4) (E-n) have no positive solutions, respectively. Moreover, we shall demonstrate that f cannot be a superlinear function.