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Zbl 1180.34069
Sun, Shurong; Han, Zhenlai; Zhang, Chenghui
Oscillation of second-order delay dynamic equations on time scales. (English)
[J] J. Appl. Math. Comput. 30, No. 1-2, 459-468 (2009). ISSN 1598-5865; ISSN 1865-2085/e

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 {\it 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 2000:: *34K11 Oscillation theory of functional-differential equations
34N05
39A10 Difference equations

Keywords: oscillation; second order; delay dynamic equations; time scale

Citations: Zbl 1082.34032

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