Abstract

Consider the first order linear delay differential equation x0(t) + p(t)x(τ(t)) = 0, t ≥ t0, where p is a continuous function of nonnegative real numbers and the argument τ(t) is not necessarily monotone. Based on an iterative technique, a new oscillation criterion is established when the well-known oscillation conditions limsupt→∞ t τ(t)p(s)ds > 1 and liminft→∞ t τ(t)p(s)ds > 1 e are not satisfied. An example, numerically solved in MATLAB, is also given to illustrates the applicability and strength of the obtained condition over known ones.