Oscillation results for second-order nonlinear neutral delay dynamic equations on time scales. (English) Zbl 1128.34042

Saker, Samir H.; Agarwal, Ravi P.; O’Regan, Donal

Appl. Anal. 86, No. 1, 1-17 (2007).

Summary: We consider the second-order nonlinear neutral delay dynamic equation
\[ \left(r(t)([y(t)+p(t)y(\tau(t))]^\Delta)^\gamma\right)^\Delta+f(t,y(\delta(t)))= 0, \]
on a time scale \(\mathbb T\) and establish some new oscillation and nonoscillation criteria. Also from these we deduce the Leighton-Wintner, Hille-Kneser, Kamenev, and Philos types oscillation criteria.
Some examples are considered to illustrate the main results.

MSC:

34K11	Oscillation theory of functional-differential equations
34K40	Neutral functional-differential equations
39A10	Additive difference equations

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