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

Voir la notice de l'article provenant de la source Cambridge University Press

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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[1] 1. Bellman, R., Stability Theory of Differential Equations. (McGraw Hill, 1953). Google Scholar

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