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On oscillation and asymptotic behaviour of solutions of forced first-order neutral differential equations. (English) Zbl 0995.34058

Here, sufficient conditions are obtained under which every solution to \[ [y(t)\pm y(t-\tau)]'\pm Q(t)G(y(t-\sigma))=f(t), \quad t\geq 0, \] oscillates or tends to zero or to \(\pm \infty\) as \(t\longrightarrow \infty\). Usually, these conditions are stronger than \[ \int_{0}^{\infty}Q(t) dt=\infty.\tag{1} \] An example is given to show that the condition (1) is not enough to arrive at the above conclusion. The existence of a positive (or negative) solution to \[ [y(t)-y(t-\tau)]'+Q(t)G(y(t-\sigma))=f(t) \] is considered.

MSC:

34K11 Oscillation theory of functional-differential equations
34K40 Neutral functional-differential equations
34K25 Asymptotic theory of functional-differential equations
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References:

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