Abstract
In this paper, we are interested in studying the periodic behavior of solutions of nonlinear difference equations. We used a new method to find the necessary and sufficient conditions for the existence of periodic solutions. Through examples, we compare the results of this method with the usual method.
Highlights
Difference equations are recognized as descriptions of the observed evolution of a phenomenon, where the majority of measurements of a time-evolving variable are discrete
Grove and Ladas [9] studied the periodic character of solutions of many difference equations of higher order
This paper aims to shed light on the study of the existence or nonexistence of periodic solutions for difference equations
Summary
Difference equations are recognized as descriptions of the observed evolution of a phenomenon, where the majority of measurements of a time-evolving variable are discrete. Grove and Ladas [9] studied the periodic character of solutions of many difference equations of higher order. Their book presented their findings along with some thought-provoking questions and many open problems and conjectures worthy of investigation. Abdelrahman et al [1] and Moaaz [25] studied the asymptotic behavior of the solutions of general equation wn+1 = awn−l + bwn−k + f (wn−l , wn−k ) , where a and b are nonnegative real number. We describe and modify the new method in Elsayed [12] We use this new method to study the existence of periodic solutions of the general class of difference equation. Through examples, we compare the results of this method with the usual method
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