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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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