The oscillatory behavior of solutions of the neutral difference equations with nonlinear neutral term, is studied in the case when c~ :fi 1. A necessary and sufficient oscillatory conditions for the case 0 < a < 1 and an almost "sharp" oscillatory and nonoseillatory criteria for the case a > i are
Oscillation of solutions for second-order nonlinear difference equations with nonlinear neutral term
โ Scribed by Zhenguo Zhang; Jianfeng Chen; Caishun Zhang
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 290 KB
- Volume
- 41
- Category
- Article
- ISSN
- 0898-1221
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โฆ Synopsis
Some Riccati type difference inequalities are given for the second-order nonlinear difference equations with nonlinear neutral term A(anA(Xn -4-~(vt, xr,.))) + qnf(xg,.) = 0 and using these inequalities, we obtain some oscillation criteria for the above equation. (~) 2001 Elsevier Science Ltd. All rights reserved.
๐ SIMILAR VOLUMES
Several oscillation criteria are established for the second-order damped nonlinear difference equation where a > 0 is any quotient of odd integers, {pโข} and {qn} are real sequences, and f E C(R, R) such that xf(x) > 0 for x # 0. Several examples which dwell upon the importance of our results are al
ln this paper, we shall establish relations between the oscillation of second-order nonlinear difference equations with damped term and the oscillation of their linear limiting equations.
In this paper, discrete inequalities are used to offer sufficient conditions for oscillation of all solutions of second-order nonlinear difference equations with alternating coefficients. @ 2000 Elsevier Science Ltd. All rights reserved.
In this paper we consider the second order nonlinear difference equation ร 4 nondecreasing, and uf u ) 0 as u / 0, q is a real sequence. Some new n ลฝ . sufficient conditions for the oscillation of all solutions of 1 are obtained.