Opuscula Math. 42, no. 6 (2022), 769-791
https://doi.org/10.7494/OpMath.2022.42.6.769

 
Opuscula Mathematica

New oscillation conditions for first-order linear retarded difference equations with non-monotone arguments

Emad R. Attia
Bassant M. El-Matary
George E. Chatzarakis

Abstract. In this paper, we study the oscillatory behavior of the solutions of a first-order difference equation with non-monotone retarded argument and nonnegative coefficients, based on an iterative procedure. We establish some oscillation criteria, involving \(\lim \sup\), which achieve a marked improvement on several known conditions in the literature. Two examples, numerically solved in MAPLE software, are also given to illustrate the applicability and strength of the obtained conditions.

Keywords: oscillation, difference equations, non-monotone argument.

Mathematics Subject Classification: 39A10, 39A21.

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  • Emad R. Attia (corresponding author)
  • ORCID iD https://orcid.org/0000-0002-7978-5386
  • Prince Sattam Bin Abdulaziz University, College of Sciences and Humanities in Alkharj, Department of Mathematics, Alkharj 11942, Saudi Arabia
  • Damietta University, Faculty of Science, Department of Mathematics, New Damietta 34517, Egypt
  • Bassant M. El-Matary
  • ORCID iD https://orcid.org/0000-0003-4525-156X
  • Qassim University, College of Science and Arts, Department of Mathematics, Al-Badaya, Buraidah, Saudi Arabia
  • Damietta University, Faculty of Science, Department of Mathematics, New Damietta 34517, Egypt
  • George E. Chatzarakis
  • ORCID iD https://orcid.org/0000-0002-0477-1895
  • Department of Electrical and Electronic Engineering Educators, School of Pedagogical and Technological, Education (ASPETE), Athens, Marousi 15122, Athens, Greece
  • Communicated by Josef Diblík.
  • Received: 2021-12-26.
  • Revised: 2022-08-06.
  • Accepted: 2022-08-08.
  • Published online: 2022-11-24.
Opuscula Mathematica - cover

Cite this article as:
Emad R. Attia, Bassant M. El-Matary, George E. Chatzarakis, New oscillation conditions for first-order linear retarded difference equations with non-monotone arguments, Opuscula Math. 42, no. 6 (2022), 769-791, https://doi.org/10.7494/OpMath.2022.42.6.769

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