Oscillation of deviating differential equations

Consider the first-order linear delay (advanced) differential equation x'(t)+p(t)x( τ(t)) =0(x'(t)-q(t)x(σ(t)) =0), t≥ t_0, where p $(q)$ is a continuous function of nonnegative real numbers and the argument τ(t) (σ(t)) is not necessarily monotone. Based on an iterative technique, a new oscillation criterion is established when the well-known conditions t→∞∫τ(t)^tp(s) { d}s>1(t→∞∫_tσ(t)q(s) { d}s>1) and t→∞∫τ(t)^tp(s) { d}s>1{}(t→∞∫_tσ(t)q(s) { d}s>1{}) are not satisfied. An example, numerically solved in MATLAB, is also given to illustrate the applicability and strength of the obtained condition over known ones.