Abstract
In this paper we obtain sharp conditions of oscillation and. nonoscillation of, the functional equation
x(g(t)) = P(t)x(t) + Sigma(i=1)(m) Q(i) (t)x(gk(i+1)(t))
where k(i) greater than or equal to1 are positive integer, P, Q(i) is an element of C([0, infinity), (0, infinity)], i = 1, 2,..., m, g is an element of C([0, infinity), (0, infinity)], g(t) < t and lim(t-->infinity)g(t) = infinity. Our results improve and extend the known results in the recent literature.