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Kamenev-type oscillation criteria for second-order linear delay dynamic equations. (English) Zbl 1104.34026
Summary: We establish Kamenev-type criteria for oscillation of the second-order delay dynamic equation \[ \bigl(r(t)x^\Delta(t)\bigr)^\Delta+p(t)x \bigl(\tau(t) \bigr)=0,\;t\in\mathbb{T}, \] where \(\mathbb{T}\) is a time scale. Our results are not only new for differential and difference equations, but are also new for the generalized difference and \(q\)-difference equations and many other dynamic equations on time scales. Our results are new for delay equations and extend some recent results of Medico and Kong. An example is given to illustrate the main results.

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
39A10 Additive difference equations
34K05 General theory of functional-differential equations
34K11 Oscillation theory of functional-differential equations