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Iterative oscillation criteria for first-order difference equations with non-monotone advanced arguments. (English) Zbl 1498.39013

Summary: Consider the first-order linear advanced difference equation of the form \[\nabla x(n)-q(n)x(\sigma (n))=0, \qquad n\in{\mathbb{N}}, \] where \((q(n))_{n\ge 1}\) is a sequence of nonnegative real numbers and \((\sigma (n))_{n\ge 1}\) is a sequence of integers such that \(\sigma (n)\ge n+1,\) for all \(n\in{\mathbb{N}} \). Based on an iterative procedure, new oscillation criteria, involving \(\lim \sup \), are established in the case of non-monotone advanced argument. Our conditions essentially improve several known results in the literature. Examples, numerically solved in Maple software, are also given to illustrate the applicability and strength of the obtained conditions over known ones.

MSC:

39A21 Oscillation theory for difference equations

Software:

Maple
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Full Text: DOI

References:

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