Oscillation criteria for nonlinear functional neutral dynamic equations on time scales. (English) Zbl 1193.34135

Erbe, Lynn; Hassan, Taher S.; Peterson, Allan

J. Difference Equ. Appl. 15, No. 11-12, 1097-1116 (2009).

The following second-order nonlinear functional dynamic equation on a time scale \(\mathbb T\)
\[ (r(t)[(x(t)\pm p(t)x(\eta(t)))^\Delta ]^\gamma )^\Delta +f(t,x(g(t))) = 0 \]
is considered, where \(\gamma\) is the quotient of odd positive integers, \(r\) and \(p\) are positive rd-continuous functions on \(\mathbb T\), \(\eta\), \(g: \mathbb T\to \mathbb T\), \(\eta (t)\leq t\), and \(\lim_{t\to \infty} \eta(t)= \lim_{t\to \infty} g(t)=\infty\). Oscillation criteria are obtained. Several examples are also given.

Reviewer: Satoshi Tanaka (Okayama)

MSC:

34K11	Oscillation theory of functional-differential equations
34N05	Dynamic equations on time scales or measure chains

Keywords:

Oscillation; dynamic equations; neutral

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