# Frequent oscillation in a nonlinear partial difference equation

Open Mathematics (2007)

- Volume: 5, Issue: 3, page 607-618
- ISSN: 2391-5455

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topJun Yang, Yu Zhang, and Sui Cheng. "Frequent oscillation in a nonlinear partial difference equation." Open Mathematics 5.3 (2007): 607-618. <http://eudml.org/doc/269536>.

@article{JunYang2007,

abstract = {This paper is concerned with a class of nonlinear delay partial difference equations with variable coefficients, which may change sign. By making use of frequency measures, some new oscillatory criteria are established. This is the first time oscillation of these partial difference equations is discussed by employing frequency measures.},

author = {Jun Yang, Yu Zhang, Sui Cheng},

journal = {Open Mathematics},

keywords = {partial difference equations; frequency measures; frequently oscillatory solution; unsaturated solution; oscillatory and periodic solutions},

language = {eng},

number = {3},

pages = {607-618},

title = {Frequent oscillation in a nonlinear partial difference equation},

url = {http://eudml.org/doc/269536},

volume = {5},

year = {2007},

}

TY - JOUR

AU - Jun Yang

AU - Yu Zhang

AU - Sui Cheng

TI - Frequent oscillation in a nonlinear partial difference equation

JO - Open Mathematics

PY - 2007

VL - 5

IS - 3

SP - 607

EP - 618

AB - This paper is concerned with a class of nonlinear delay partial difference equations with variable coefficients, which may change sign. By making use of frequency measures, some new oscillatory criteria are established. This is the first time oscillation of these partial difference equations is discussed by employing frequency measures.

LA - eng

KW - partial difference equations; frequency measures; frequently oscillatory solution; unsaturated solution; oscillatory and periodic solutions

UR - http://eudml.org/doc/269536

ER -

## References

top- [1] B.G. Zhang and Q.J. Xing: “Oscillation of certain partial difference equations”, J. Math. Anal. Appl., to appear. Zbl1115.39018
- [2] C.J. Tian, S.L. Xie and S.S. Cheng: “Measures for oscillatory sequences”, Comput. Math. Appl., Vol. 36, (1998), pp. 149–161. http://dx.doi.org/10.1016/S0898-1221(98)80017-5 Zbl0933.39024
- [3] S.S. Cheng, Partial Difference Equations, Taylor and Francis, 2003.
- [4] Z.Q. Zhu and S.S. Cheng: “Frequent oscillation in a neutral difference equation”, Southeast Asian Bull. Math., Vol. 29, (2005), pp. 627–634.
- [5] Z.Q. Zhu and S.S. Cheng: “Frequently oscillatory solutions for multi-level partial difference equations”, Int. Math. Forum, Vol. 1, (2006), pp. 1497–1509. Zbl1119.39013
- [6] Z.Q. Zhu and S.S. Cheng: “Unsaturated solutions for partial difference equations with forcing terms”, Cent. Eur. J. Math., to appear. Zbl1118.39006
- [7] E.F. Beckenbach and R. Bellman: Inequalities, Random House, N. Y. Berlin, 1961.
- [8] H. Halberstam and K.F. Roth: Sequences, Springer-Verlag, 1983.
- [9] I. Niven: “The asymptotic density of sequences”, Bull. Amer. Math. Soc., Vol. 57, (1951), pp. 420–434. http://dx.doi.org/10.1090/S0002-9904-1951-09543-9 Zbl0044.03603
- [10] C.J. Tian and S.S. Cheng: “Frequent convergence and applications”, Dyn. Cont. Dis. Ser. A, Vol. 13, (2006), pp. 653–668. Zbl1116.26001

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