Wong’s oscillation theorem for second-order delay differential equations - Özbekler, A.; Zafer, A. (Нелінійні коливання, 2016)
Let H(t) := ∫1/(r(s)z²(s)) (∫z(k)f(k)dk) ds, where z is a positive solution of (r(t)x')' + q(t)x = 0, t ≥ a, satisfying ∫1 / (r(s)z²(s)) ds < ∞. It is well known that, see [J. S. W. Wong, J. Math. Anal. and Appl. — 1999. — 231. — P. 235 – 240], if limt→∞ H(t) = − lim t→∞ H(t) = ∞, then every solution of (r(t)x') + q(t)x = f(t) is oscillatory. In this paper we extend Wong’s result to delay differential equations of the form (r(t)x' (t))' + q(t)x(τ(t)) = f(t). It is observed that the oscillation behavior may be altered due to presence of the delay. Extensions to Emden – Fowler type delay differential equations are also discussed.