## 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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