## Oscillation and asymptotic behaviour of a higher order neutral differential equation with positive and negative coefficients.(English)Zbl 1171.34043

Summary: We obtain necessary and sufficient conditions so that every solution of
$\big(y(t)- p(t) y(r(t))\big)^{(n)}+ q(t)G( y(g(t)))-u(t)H(y(h(t))) = f(t)$
oscillates or tends to zero as $$t \to \infty$$, where $$n$$ is an integer $$n \geq 2, q>0, u\geq 0$$. Both bounded and unbounded solutions are considered in this paper. The results hold also when $$u\equiv 0, f(t)\equiv 0$$, and $$G(u)\equiv u$$. This paper extends and generalizes some recent results.

### MSC:

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