## Oscillation of second-order delay dynamic equations on time scales.(English)Zbl 1180.34069

J. Appl. Math. Comput. 30, No. 1-2, 459-468 (2009); erratum ibid. 39, No. 1-2, 551-554 (2012).
Summary: By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order nonlinear delay dynamic equations
$\bigl(p(t)\bigl(x^{\Delta}(t)\bigr)^{\gamma}\bigr)^{\Delta}+q(t)f\bigl(x\bigl(\tau(t)\bigr)\bigr)=0$
on a time scale $$\mathbb{T}$$, here $$\gamma \geq 1$$ is a quotient of odd positive integers with $$p$$ and $$q$$ real-valued positive rd-continuous functions defined on $$\mathbb{T}$$. Our results improve and extend some results established by S. H. Saker [J. Comput. Appl. Math. 177, No. 2, 375–387 (2005; Zbl 1082.34032)] but also unify the oscillation of the second order nonlinear delay differential equation and the second order nonlinear delay difference equation.

### MSC:

 34K11 Oscillation theory of functional-differential equations 34N05 Dynamic equations on time scales or measure chains 39A10 Additive difference equations

### Keywords:

oscillation; second order; delay dynamic equations; time scale

Zbl 1082.34032
Full Text:

### References:

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