Neutral delay differential equations with positive and negative coefficients. (English) Zbl 0618.34063

Consider the neutral delay differential equation \[ (1)\quad \frac{d}{dt}[y(t)+py(t-\tau)]+q_ 1y(t-\sigma _ 2)-q_ 2y(t-\sigma _ 2)=0 \] where \[ (2)\quad p\in R-\{0\},\quad q_ 1,q_ 2\in (0,\infty),\quad \tau \in (0,\infty),\quad \sigma _ 1,\sigma _ 2\in [0,\infty). \] We study the asymptotic behavior of the nonoscillatory solutions of (1) and we obtain sufficient conditions for the oscillation of all solutions, all bounded solutions, and all unbounded solutions of (1).


34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34K25 Asymptotic theory of functional-differential equations
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