## Oscillation of a higher order neutral differential equation with a sub-linear delay term and positive and negative coefficients.(English)Zbl 1212.34191

Summary: We obtain sufficient conditions for every solution of the differential equation $[y(t)-p(t)y(r(t))]^{(n)}+v(t)G(y(g(t)))-u(t)H(y(h(t)))=f(t)$ to oscillate or to tend to zero as $$t$$ approaches infinity. In particular, we extend the results of B. Karpuz, L. N. Padhy and R. Rath [Electron. J. Differ. Equ. 113, Paper No. 113 (2008; Zbl 1171.34043)] to the case when $$G$$ has sub-linear growth at infinity. Our results also apply to the neutral equation $[y(t)-p(t)y(r(t))]^{(n)}+q(t)G(y(g(t)))=f(t)$ when $$q(t)$$ has sign changes. Both bounded and unbounded solutions are considered here.

### MSC:

 34K11 Oscillation theory of functional-differential equations 34K40 Neutral functional-differential equations

Zbl 1171.34043
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