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

Abstract

It might be thought that, as far as the oscillation of solutions is concerned, the behaviour of and would 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/2t 2 i.e. This equation has the non-oscillatory solution y(t) = t 1/2 although all solutions of are oscillatory [1, p. 121].