A survey on the oscillation of differential equations with several deviating 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. A survey on the oscillation of all solutions to this equation is presented in the case of several non-monotone arguments and especially when well-known oscillation conditions are not satisfied. Examples illustrating the results are given.