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Oscillatory and asymptotic behavior of certain fourth order difference equations. (English) Zbl 0602.39003

From authors’ introduction: This note is concerned with the solutions of the fourth order linear difference equation \[ \Delta (\Delta^ 3u_ n+p_ nu_{n+2})+p_ n\Delta u_{n+1}+q_ nu_{n+2}=0 \] where \(\Delta\) denotes the differencing operator, i.e. \(\Delta x_ n=x_{n+1}-x_ n\). While no sign conditions are explicitly stated for the real sequences \(\{p_ n\}\), it will be assumed that \(q_ n>0\) for each n.
Reviewer: P.Reichensperger

MSC:

39A10 Additive difference equations
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