New oscillation criteria for odd order neutral equations. (English) Zbl 0860.34040

Shen, J. H.

J. Math. Anal. Appl. 201, No. 2, 387-395 (1996).

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 \(\int^\infty_{t_0} s^{n-1} Q(s)ds=\infty\).

Reviewer: Wang Zhicheng (Changsha)

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

Keywords:

oscillation criteria; \(n\)th order neutral differential equation