Upper and lower limit oscillation conditions for first-order difference equations


Proceedings of the Edinburgh Mathematical Society, vol.65, no.3, pp.618-631, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 65 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.1017/s0013091522000244
  • Journal Name: Proceedings of the Edinburgh Mathematical Society
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, MathSciNet, zbMATH
  • Page Numbers: pp.618-631
  • Keywords: delay difference equation, general argument, oscillation
  • Akdeniz University Affiliated: Yes


Copyright © 2022 The Author(s).where (p(n)) is a sequence of non-negative real numbers, (τ(n)) is a sequence of integers such that τ(n) < n for n ∈ N, and limn→∞ τ(n) = ∞. Under the assumption that the deviating argument is not necessarily monotone, we obtain some new oscillation conditions and improve the all known results for the above equation in the literature, involving only upper and only lower limit conditions. Two examples illustrating the results are also given.