A Note on an Oscillation Criterion for an Equation with a Functional Argument

Abstract

It might be thought that, as far as the oscillation of solutions is concerned, the behaviour ofandwould be the same as long as t - α(t) → ∞ as t→∞. To motivate the theorem presented in this note, we show first that this is not the case. Consider the above equation with α(t) = 3t/4, a(t) = l/2t2 i.e.This equation has the non-oscillatory solution y(t) = t1/2 although all solutions ofare oscillatory [1, p. 121].