Difference calculus with applications to difference equations. (English) Zbl 0592.39001

General inequalities 4, Mem. E. F. Beckenbach, 4th Int. Conf., Oberwolfach/Ger. 1983, ISNM 71, 95-110 (1984).
[For the entire collection see Zbl 0573.00004.]
The paper is primarily concerned with n-th order nonlinear difference equations of the form \[ \Delta^ nx(t)+\sum^{m}_{i=1}f_ i(t)F_ i(x(t),\Delta x(t),...,\Delta^{n-1}(t))=0, \] t being a nonnegative integer. Discrete analogues are presented of some known oscillation theorems for differential equations. The proofs are based on discrete versions of Taylor’s formula, l’Hospital’s rule and a theorem of Kneser which are derived in this paper.
Reviewer: B.Aulbach


39A10 Additive difference equations
39A11 Stability of difference equations (MSC2000)


Zbl 0573.00004