Oscillation and nonoscillation of neutral difference equations with positive and negative coefficients. (English) Zbl 0958.39016
The authors establish several new sufficient conditions for the oscillation of all solutions of
\[
\Delta(x_n-c_n x_{n-\tau}) +p_nx_{n-k}-q_nx_{n-\ell} =0
\]
with \(p_n-q_{n-k+\ell}\geq 0\) and not identically zero. Also existence theorems for the positive solutions are obtained.
For related results see the papers of M.-P. Chen and B. G. Zhang [Bull. Inst. Math., Acad. Sin. 22, 295-306 (1994; Zbl 0817.39003)] and B. G. Zhang and H. Wang [Chin. J. Math. 24, No. 4, 377-393 (1996; Zbl 0868.39005)].
For related results see the papers of M.-P. Chen and B. G. Zhang [Bull. Inst. Math., Acad. Sin. 22, 295-306 (1994; Zbl 0817.39003)] and B. G. Zhang and H. Wang [Chin. J. Math. 24, No. 4, 377-393 (1996; Zbl 0868.39005)].
Reviewer: E.Thandapani (Salem)
MSC:
| 39A11 | Stability of difference equations (MSC2000) |
References:
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| [3] | Chen, M.-P.; Zhang, B. G., Oscillation and comparison theorems of difference equations with positive and negative coefficients, Bulletin of the Institute of Math. Academia Sinica, 22, 4, 295-306 (1994) · Zbl 0817.39003 |
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