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New oscillation criteria for odd order neutral equations. (English) Zbl 0860.34040
The paper gives some new oscillation criteria for all solutions of the \(n\)th order neutral differential equation \[ {d^n \over {dt^n}} (x(t)- P(t) x(t-\tau))+ Q(t) x(t-\sigma)=0 \] where \(P\in C([t_0,\infty), \mathbb{R})\), \(Q\in C([t_0,\infty), \mathbb{R}^+)\), \(\tau>0\), \(\sigma\geq 0\) and \(n\) is odd. The results obtained do not need the usual hypothesis \(\int^\infty_{t_0} s^{n-1} Q(s)ds=\infty\).

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