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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
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References:
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