Oscillation criteria for even order neutral differential equations. (English) Zbl 0933.34075

Zafer, A.

Appl. Math. Lett. 11, No. 3, 21-25 (1998).

Summary: Oscillation criteria are given for even-order neutral type differential equations of the form \[ \biggl[x(t) +a(t)x\bigl( \tau(t)\bigr) \biggr]^{(n)} +f\biggl(t,x(t),x \bigl(\sigma(t)\bigr)\biggr)=0, \] with \(f(t,x, y)\in C([0, \infty)\times \mathbb{R}^2,\mathbb{R})\) and \(a,\tau, \sigma\in C([0,\infty), \mathbb{R})\) such that \(0\leq a(t)<1\), \(\tau(t)<t\), \(\sigma(t)\leq t\), and \(\lim_{t \to\infty} \tau(t)=\lim_{t \to\infty} \sigma(t)= \infty\).

MSC:

34K11	Oscillation theory of functional-differential equations
34K40	Neutral functional-differential equations

Keywords:

oscillation; even-order neutral type differential equations

References:

[1]	Hale, J. K., Theory of Functional Differential Equations (1977), Springer-Verlag: Springer-Verlag New York · Zbl 0425.34048
[2]	Bainov, D. D.; Mishev, D. P., Oscillation Theory for Neutral Differential Equations with Delay (1992), IOP Publishing: IOP Publishing Bristol, UK · Zbl 0789.35015
[3]	Ladde, G. S.; Lakshmikantham, V.; Zhang, B. G., Oscillation Theory of Differential Equations with Deviating Arguments (1987), Marcel Dekker: Marcel Dekker New York · Zbl 0832.34071
[4]	Kusano, T.; Onose, H., Nonlinear oscillation of a sublinear delay equation of arbitrary order, Pro. Amer. Math. Soc., 40, 219-224 (1973) · Zbl 0268.34075
[5]	Dahiya, R. S.; Zafer, A., Asymptotic behavior and oscillation in higher order differential equations with retarded arguments, Acta Math. Hungar., 76, 3, 257-266 (1997) · Zbl 0907.34051
[6]	Kiguradze, I. T., On the oscillation of solutions of equation \(d^mudt^m\)+a(t)\(u^m\) sgn u = 0\), Mat. Sb., 65, 172-187 (1964) · Zbl 0135.14302