Oscillation of second order neutral dynamic equations with deviating arguments on time scales. (English) Zbl 1448.34167
Summary: In this paper, we consider the following second order neutral dynamic equations with deviating arguments on time scales:
\[
\bigl(r(t) \bigl(z^{\Delta}(t)\bigr)^{\alpha}\bigr)^{\Delta}+q(t)f \bigl(y\bigl(m(t)\bigr)\bigr)=0,
\]
where \(z(t)=y(t)+p(t)y(\tau(t))\), \(m(t)\leq t\) or \(m(t)\geq t\), and \(\tau(t)\leq t\). Some new oscillatory criteria are obtained by means of the inequality technique and a Riccati transformation. Our results extend and improve many well-known results for oscillation of second order dynamic equations. Some examples are given to illustrate the main results.
MSC:
| 34N05 | Dynamic equations on time scales or measure chains |
| 26E70 | Real analysis on time scales or measure chains |
| 34C10 | Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations |
| 34K40 | Neutral functional-differential equations |
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