Discussiones Mathematicae Differential Inclusions 15(2) (1995) 213-219

[BIBTex]

NECESSARY AND SUFFICIENT CONDITIONS FOR OSCILLATIONS OF DELAY PARTIAL DIFFERENCE EQUATIONS

Bing Gen Zhang

Department of Applied Mathematics Ocean University of Qingdao
Qingdao 266003, China

Shu Tang Liu

Department of Mathematics Binzhou Normal College
Binzhou, Shandong, 256604, China

Abstract

This paper is concerned with the delay partial difference equation

(1)

Am+1,n+Am,n+1-Am,n+

u
Σ
i = 1
piAm-ki, n-li = 0,

where pi are real numbers, ki and li are nonnegative integers, u is a positive integer. Sufficient and necessary conditions for all solutions of (1) to be oscillatory are obtained.

Keywords: partial difference equations, oscillation, characteristic equation.

1991 Mathematics Subject Classification: 39A10.

References

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