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Zbl 1062.34068
Agarwal, Ravi P.; O'Regan, Donal; Saker, S.H.
Oscillation criteria for second-order nonlinear neutral delay dynamic equations. (English)
[J] J. Math. Anal. Appl. 300, No. 1, 203-217 (2004). ISSN 0022-247X

Summary: We establish some oscillation criteria for the second-order nonlinear neutral delay dynamic equation $$\left(r(t)\left(\left(y(t)+ p(t)y(t-\tau)\right)^\Delta \right)^\gamma\right)^\Delta+f\bigl(t,y(t-\delta)\bigr)=0$$ on a time scale $\bbfT$; here, $\gamma >0$ is a quotient of odd positive integers with $r(t)$ and $p(t)$ real-valued positive functions defined on $\bbfT$. To the best of our knowledge nothing is known regarding the qualitative behavior of these equations on time scales, so this paper initiates the study.

MSC 2000:: *34K11 Oscillation theory of functional-differential equations
34K40 Neutral equations
39A12 Discrete version of topics in analysis

Keywords: Oscillation; Neutral; Delay; Dynamic equations; Time scale

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