New oscillation results for first-order nonlinear difference equations with retarded arguments

Volume 35, Issue 2, pp 241--255 https://dx.doi.org/10.22436/jmcs.035.02.08

Publication Date: May 08, 2024 Submission Date: January 10, 2024 Revision Date: April 07, 2024 Accteptance Date: April 15, 2024

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Authors

E. R. Attia - Department of Mathematics, College of Sciences and Humanities, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia. - Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt.

Abstract

In this paper, the oscillation of the first-order nonlinear delay difference equation \[\Delta y(l)+ a(l) y(l+1)+b(l) f(y(\vartheta(l)))=0,\quad l\in \mathbb{N}_0, \] is studied. Some explicit oscillation results of liminf and limsup are given. We obtain many new results using the comparison between both first-order delay linear and nonlinear difference equations. We give an illustrative example to demonstrate the strength and simplicity of our results.

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Keywords

• Nonlinear difference equations
• differential equations
• oscillation
• nonmonotone delays

MSC

•  34C10
•  34K11
•  34K05

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