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

Ladas, G.

J. Math. Anal. Appl. 153, No. 1, 276-287 (1990).

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 \(k_ i's\).

Reviewer: Baotong Cui (Binzhou)

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)

Keywords:

explicit conditions; oscillation; difference equation; differential difference equations

References:

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