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Oscillatory behaviour of solutions of forced neutral differential equations. (English) Zbl 0874.34063
The authors study some qualitative properties of solutions of forced neutral delay differential equations of the form $\left[x(t)+\sum_{i=1}^l p_{i}(t)x(t-\tau_{i})\right]^{(n)} + \delta\sum_{j=1}^m q_{j}(t)x(t-\sigma_{j}) = f(t) \tag{1}$ and $\left[x(t) +\sum_{i=1}^{l} p_{i}(t)g_{i}(x(t-\tau_{i}))\right]^{(n)} + \delta\sum_{j=1}^m q_{j}(t)h_{j}(x(t-\sigma_{j})) = f(t)\tag{2}$ where $$p_{i}, q_{j}, f \in C([t_{0},\infty),\mathbb{R})$$, $$g_{i}, h_{j} \in C(\mathbb{R},[0,\infty))$$ are such that $$xg_{i}(x) > 0,\;xh_{j}(x) > 0$$, for $$x \neq 0$$ and $$\tau_{i}, \sigma_{j} \geq 0.$$ They establish some sufficient conditions for oscillation of all solutions of (1) and (2). Also, in the case of a nonoscillatory situation, they provide some results on their asymptotic behaviour.

##### MSC:
 34K40 Neutral functional-differential equations 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34K11 Oscillation theory of functional-differential equations
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