Oscillation criteria for differential equations with several retarded arguments

Consider the first-order linear differential equation with several retarded arguments x'(t) + Sigma(m)(i=1) p(i)(t)x(tau(i)(t)) = 0, t >= t(0), where the functions p(i), tau(i) is an element of C([t(0), infinity), R+), for every i = 1, 2, ... , m, tau(i)(t) <= t for t >= t(0) and lim(t ->infinity) tau(i)(t) = infinity. In this paper the state-of-the-art on the oscillation of all solutions to these equations is reviewed and new sufficient conditions for the oscillation are established, especially in the case of nonmonotone arguments. Examples illustrating the results are given.