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 (Q638133)
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scientific article; zbMATH DE number 5946516
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | 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 |
scientific article; zbMATH DE number 5946516 |
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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)
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9 September 2011
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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 \(n \rightarrow \infty\).
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oscillation
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linear discrete delayed equation
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positive solution
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