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Zbl 1006.39011
Grzegorczyk, G.; Werbowski, J.
Oscillation of higher-order linear difference equations. (English)
[J] Comput. Math. Appl. 42, No.3-5, 711-717 (2001). ISSN 0898-1221

This paper is concerned with the oscillatory and asymptotic behavior of the solutions of the linear higher-order difference equation of the form $$\Delta ^{m}x(n)+p(n)x(n-k)=0.$$ Two interesting sufficient conditions (one involving the $\limsup$ and the other the $\liminf$) are established. Two examples illustrating the significance of the results by comparing to known results are given.
[Ioannis P.Stavroulakis (Ioannina)]

MSC 2000:: *39A11 Stability of difference equations

Keywords: oscillation; higher-order linear difference equations; asymptotic

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