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Keywords:
oscillatory solution; neutral differential equation; asymptotic behaviour
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 Karpuz, Rath and Padhy (2008) 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 consideted here; thus some known results are expanded.
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