Geodesic
Interval Oscillation for Second Order Nonlinear Differential Equations with a Damping Term
Serdica Mathematical Journal, Tome 34 (2008) no. 4, pp. 715-732.

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It is the purpose of this paper to give oscillation criteria for the second order nonlinear differential equation with a damping term (a(t) y′(t))′ + p(t)y′(t) + q(t) |y(t)| α−1 y(t) = 0, t ≥ t0, where α ≥ 1, a ∈ C1([t0,∞);(0,∞)) and p,q ∈ C([t0,∞);R). Our results here are different, generalize and improve some known results for oscillation of second order nonlinear differential equations that are different from most known ones in the sencse they are based on the information only on a sequence of subintervals of [t0,∞), rather than on the whole half-line and can be applied to extreme cases such as ∫t0∞ q(t) dt = − ∞. Our results are illustrated with an example.
Keywords: Interval Oscillation, Second Order, Nonlinear Differential Equations 
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Hassan, Taher S. Interval Oscillation for Second Order Nonlinear Differential Equations with a Damping Term. Serdica Mathematical Journal, Tome 34 (2008) no. 4, pp. 715-732. http://geodesic.mathdoc.fr/item/SMJ2_2008_34_4_a1/