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Oscillation behaviour of solutions of neutral delay differential equations. (English) Zbl 0697.34061
Summary: We study oscillatory behaviour of solutions of the neutral delay differential equation \[ d/dt[x(t)-\sum^{n}_{i=1}p_ i(t)x(t-a_ i)]+q_ 0(t)x(t)+\sum^{m}_{j=1}q_ j(t)x(t-b_ j)=0,\quad t\geq t_ 0. \] We generalize the results of G. Ladas and Y. G. Sficas [Can. Math. Bull. 29, 438-445 (1986; Zbl 0566.34054)] for the equation \[ d/dt[x(t)-px(t-\tau)]+Q(t)x(t-\sigma)=0,\quad t\geq t_ 0, \] where p, \(\tau\), and \(\sigma\) are positive constants, \(Q\in C([t_ 0,\infty),{\mathbb{R}}^+)\).

MSC:
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
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