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.


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


Zbl 1171.34043
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