# Necessary and sufficient conditions for oscillations of delay partial difference equations

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (1995)

- Volume: 15, Issue: 2, page 213-219
- ISSN: 1509-9407

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topBing Gen Zhang, and Shu Tang Liu. "Necessary and sufficient conditions for oscillations of delay partial difference equations." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 15.2 (1995): 213-219. <http://eudml.org/doc/275970>.

@article{BingGenZhang1995,

abstract = {This paper is concerned with the delay partial difference equation
(1) $A_\{m+1,n\}+A_\{m,n+1\}-A_\{m,n\} + Σ_\{i=1\}^u p_i A_\{m-k_i, n-l_i\} = 0$
where $p_i$ are real numbers, $k_i$ and $l_i$ are nonnegative integers, u is a positive integer. Sufficient and necessary conditions for all solutions of (1) to be oscillatory are obtained.},

author = {Bing Gen Zhang, Shu Tang Liu},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {partial difference equations; oscillation; characteristic equation; partial delay difference equations; -transform technique},

language = {eng},

number = {2},

pages = {213-219},

title = {Necessary and sufficient conditions for oscillations of delay partial difference equations},

url = {http://eudml.org/doc/275970},

volume = {15},

year = {1995},

}

TY - JOUR

AU - Bing Gen Zhang

AU - Shu Tang Liu

TI - Necessary and sufficient conditions for oscillations of delay partial difference equations

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 1995

VL - 15

IS - 2

SP - 213

EP - 219

AB - This paper is concerned with the delay partial difference equation
(1) $A_{m+1,n}+A_{m,n+1}-A_{m,n} + Σ_{i=1}^u p_i A_{m-k_i, n-l_i} = 0$
where $p_i$ are real numbers, $k_i$ and $l_i$ are nonnegative integers, u is a positive integer. Sufficient and necessary conditions for all solutions of (1) to be oscillatory are obtained.

LA - eng

KW - partial difference equations; oscillation; characteristic equation; partial delay difference equations; -transform technique

UR - http://eudml.org/doc/275970

ER -

## References

top- [1] S.S. Cheng, B.G. Zhang, Qualitative theory of partial difference equations (I): Oscillation of nonlinear partial difference equations, Tamkang J. Math. 25 (3) (1994), 279-288. Zbl0809.39002
- [2] B.G. Zhang, S.T. Liu, S.S. Cheng, Oscillation of a class of delay partial difference equations, J. Difference Equations and its Applications, 1 (1995), 215-226. Zbl0856.39015
- [3] Li Xiang-ping, Partial difference equations used in the study of molecular orbits, Acta Chimica SINICA, 40 (8) (1982), 688-698.
- [4] W.G. Kelley, A.C. Peterson, Difference Equations, Academic Press, Inc., New York 1991.