On the oscillatory behavior of even order neutral delay dynamic equations on time-scales. (English) Zbl 1340.34243
Summary: We establish some new criteria for the oscillation of the even order neutral dynamic equation
\[
\left( a(t)\left( \left( x(t)-p(t)x(\tau (t))\right) ^{\Delta^{n-1}}\right) ^{\alpha}\right) ^{\Delta}+q(t)\left( x^{\sigma}(g(t))\right) ^{\lambda}=0
\]
on a time scale \(\mathbb{T}\), where \(n \geq 2\) is even, \(\alpha \) and \(\lambda \) are ratios of odd positive integers, \(a\), \(p\) and \(q\) are real valued positive rd-continuous functions defined on \(\mathbb{T}\), and \(g\) and \(\tau \) are real valued rd-continuous functions on \(\mathbb{T}\). Examples illustrating the results are included.
MSC:
34K11 | Oscillation theory of functional-differential equations |
34N05 | Dynamic equations on time scales or measure chains |
34K40 | Neutral functional-differential equations |