Geodesic
A Note on an Oscillation Criterion for anEquation with a Functional Argument
Canadian mathematical bulletin, Tome 11 (1968) no. 4, pp. 593-595

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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/2t2 i.e. This equation has the non-oscillatory solution y(t) = t1/2 although all solutions of are oscillatory [1, p. 121]. 
Waltman, Paul. A Note on an Oscillation Criterion for anEquation with a Functional Argument. Canadian mathematical bulletin, Tome 11 (1968) no. 4, pp. 593-595. doi: 10.4153/CMB-1968-071-2
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