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Nonoscillatory solutions for higher-order neutral dynamic equations on time scales. (English) Zbl 1205.34136

Summary: We study the higher-order neutral dynamic equation
\[ \{a(t)[(x(t)-p(t)x(\tau(t)))^{\Delta^m}]^\alpha\}^\Delta+f(t,x(\rho(t)))=0\text{ for }t\in[t_0,\infty)_{\mathbb T} \]
and obtain some necessary and sufficient conditions for the existence of nonoscillatory bounded solutions for this equation.

MSC:

34N05 Dynamic equations on time scales or measure chains
34K11 Oscillation theory of functional-differential equations
34K40 Neutral functional-differential equations
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References:

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