Driver, R. D.; Ladas, G.; Vlahos, P. N. Asymptotic behavior of a linear delay difference equation. (English) Zbl 0751.39001 Proc. Am. Math. Soc. 115, No. 1, 105-112 (1992). The asymptotic behavior of solutions of the equations \(x_{n+1}-x_ n=\sum^ m_{j=1}a_ j(x_{n-k_ j}-x_{n-l_ j})\) and \(y_{n+1}- y_ n=\sum^ k_{j=1}b_ jy_{n-j}\), \(n=0,1,2,\ldots,\) is obtained for the case that the characteristic equation has a dominant real root. Some examples illustrate the results. Reviewer: B.M.Agrawal (Lashkar-Gwalior) Cited in 2 ReviewsCited in 21 Documents MSC: 39A10 Additive difference equations 39A11 Stability of difference equations (MSC2000) Keywords:linear delay difference equation; asymptotic behavior; characteristic equation; dominant real root PDFBibTeX XMLCite \textit{R. D. Driver} et al., Proc. Am. Math. Soc. 115, No. 1, 105--112 (1992; Zbl 0751.39001) Full Text: DOI References: [1] N. G. de Bruijn, On some linear functional equations, Publ. Math. Debrecen 1 (1950), 129 – 134. · Zbl 0036.19501 [2] R. D. Driver, D. W. Sasser, and M. L. Slater, The equation \?\(^{\prime}\)(\?)=\?\?(\?)+\?\?(\?-\?) with ”small” delay, Amer. Math. Monthly 80 (1973), 990 – 995. · Zbl 0292.34076 · doi:10.2307/2318773 [3] G. Ladas, Ch. G. Philos, and Y. G. Sficas, Necessary and sufficient conditions for the oscillation of difference equations, Libertas Math. 9 (1989), 121 – 125. · Zbl 0689.39002 [4] M. J. Norris, unpublished notes on the delay differential equation \( x'(t) = bx(t - 1)\) where \( - 1/e \leq b < 0\), October 1967. [5] E. C. Partheniadis, Stability and oscillation of neutral delay differential equations with piecewise constant argument, Differential Integral Equations 1 (1988), no. 4, 459 – 472. · Zbl 0723.34059 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.