Necessary and sufficient conditions for oscillations of delay partial difference equations

Bing Gen Zhang; Shu Tang Liu

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

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

Abstract

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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.

How to cite

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Bing 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

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  1. [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. [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. [3] Li Xiang-ping, Partial difference equations used in the study of molecular orbits, Acta Chimica SINICA, 40 (8) (1982), 688-698. 
  4. [4] W.G. Kelley, A.C. Peterson, Difference Equations, Academic Press, Inc., New York 1991. 

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