A final result on the oscillation of solutions of the linear discrete delayed equation \({\Delta}x(n) = -p(n)x(n - k)\) with a positive coefficient. (English) Zbl 1223.39008
Summary: A linear \((k + 1)\)th-order discrete delayed equation \({\Delta}x(n) = -p(n)x(n - k)\) where \(p(n)\) is a positive sequence is considered for \(n \rightarrow \infty\). This equation is known to have a positive solution if the sequence \(p(n)\) satisfies an inequality. Our aim is to show that, in the case of the opposite inequality for \(p(n)\), all solutions of the equation considered are oscillating for \(n \rightarrow \infty\).
MSC:
| 39A21 | Oscillation theory for difference equations |
| 39A12 | Discrete version of topics in analysis |
| 34K11 | Oscillation theory of functional-differential equations |
| 39A22 | Growth, boundedness, comparison of solutions to difference equations |
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