Oscillation properties for a scalar linear difference equation of mixed type. (Q2810142)
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scientific article; zbMATH DE number 6587861
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Oscillation properties for a scalar linear difference equation of mixed type. |
scientific article; zbMATH DE number 6587861 |
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31 May 2016
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delayed difference equation
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oscillation theory
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0.9157896
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0.9090953
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0.90670866
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Oscillation properties for a scalar linear difference equation of mixed type. (English)
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The authors consider the linear difference equation of mixed type NEWLINE\[NEWLINE\Delta x(n)+\sum_{k=-p}^q a_k(n)x(n+k)=0,NEWLINE\]NEWLINE where \(\{a_k(n)\}\) are sequences of real numbers for \(k=-p,\dots,q\), and \(p>0,q\geq 0\). Various kinds of sufficient conditions which guarantee that all solutions of this equation are oscillatory are established. Nonoscillatory criteria are also proved. The final section is devoted to deriving the conditions for all positive solutions to tend to zero.
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