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On oscillatory third-order difference equations. (English) Zbl 0963.39009
The authors deal with the third-order linear difference equation \[ y_{n+3}+ r_ny_{n+2} +q_ny_{n+1} +p_ny_n= f_n, \] where \(\{r_n\}\), \(\{q_n\}\), \(\{p_n\}\) and \(\{f_n\}\) are real sequences. They provide various conditions under which all solutions to the above equation oscillate. In the homogeneous case \((f_n\equiv 0)\) they also give a sufficient condition for the existence of a nonoscillatory (positive) solution.

MSC:
39A11 Stability of difference equations (MSC2000)
39A12 Discrete version of topics in analysis
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References:
[1] Gregus M., Third Order Linear Differential Equations (1987)
[2] Hartman P., Trans. Amer. Math. Soc. 246 pp 1– (1987)
[3] DOI: 10.1016/0898-1221(94)00101-4 · Zbl 0809.39005 · doi:10.1016/0898-1221(94)00101-4
[4] Mickens R.E., Difference Equations (1987) · Zbl 1235.70006
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