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Explicit conditions for the oscillation of difference equations. (English) Zbl 0718.39002

The author considers sufficient conditions for the oscillation of all solutions of the difference equation (*) \(A_{n+1}-A_ n+\sum^{n}_{i=1}p_ iA_{n-k_ i}=0,\) \(n=0,1,2,...\), where the \(p_ i's\) are real numbers and the \(k_ i's\) are integers. Four theorems for the oscillation of the solutions of (*) are obtained by means of careful analysis and comparing equation (*) with differential difference equations. Conditions are given explicitly in terms of the \(p_ i's\) and the \(k_ i's\).

MSC:

39A10 Additive difference equations
39A12 Discrete version of topics in analysis
34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
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