Discrete oscillations. (English) Zbl 0881.39007

The paper deals with oscillation and nonoscillation criteria for the following linear difference equation \[ x_{n+1} -b(n)x_n +\sum^n_{i=1} P_i(n) x_{n-k_i}=0, \quad n=0,1,2, \dots \] with several delays. The main results provide sufficient conditions for the above equation to have nonoscillatory or oscillatory solutions. A comparison theorem and some applications are also given.


39A12 Discrete version of topics in analysis
39A10 Additive difference equations
Full Text: DOI


[1] Erbe L. H., Differential Integral Equations 2 pp 300– (1989)
[2] Ladas G., J. Appl. Math. Simulation 2 pp 101– (1989)
[3] DOI: 10.1016/0022-247X(90)90278-N · Zbl 0718.39002
[4] Qian C., Funkcialaj Ekvacioj 35 pp 581– (1992)
[5] DOI: 10.1006/jmaa.1993.1267 · Zbl 0787.39004
[6] Gyö, I. and Ladas, G. 1991. ”Oscillatory theory of delay differential equations with applications”. Oxford: Oxford University Press. · Zbl 0780.34048
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.