Oscillation results for second order neutral dynamic equations with distributed deviating arguments. (English) Zbl 1312.34143
Summary: We establish some new criteria for the oscillation of second-order nonlinear neutral dynamic equations with distributed deviating arguments of the form
\[
(r(t)|y^\Delta(t)|^{\gamma-1} y^\Delta(t))^\Delta+ \int^b_a f(t,x(\theta(t,\xi)))\,\Delta\xi= 0
\]
on a time scale \(\mathbb{T}\), where \(y(t):= x(t)+ p(t)x(r(t))\), \(\gamma\geq 1\) is a constant, \(r(t)\), \(p(t)\) are \(rd\)-continuous functions on \(\mathbb{T}\), and \(f: \mathbb{T}\times\mathbb{R}\to \mathbb{R}\) is continuous. The results obtained are illustrated with a number of examples.
MSC:
34N05 | Dynamic equations on time scales or measure chains |
34K11 | Oscillation theory of functional-differential equations |
34K40 | Neutral functional-differential equations |