On the Solutions of a General System of Difference Equations

Abstract

We deal with the solutions of the systems of the difference equationsxn+1=1/xn-pyn-p,yn+1=xn-pyn-p/xn-qyn-q, andxn+1=1/xn-pyn-pzn-p,yn+1=xn-pyn-pzn-p/xn-qyn-qzn-q,zn+1=xn-qyn-qzn-q/xn-ryn-rzn-r, with a nonzero real numbers initial conditions. Also, the periodicity of the general system ofkvariables will be considered.

Effective methods on determining the periodicity and form of solutions of some systems of non-linear difference equations

“…[2]. However, we have found that there is an error in one of the result stated in [17]. Perhaps because the result was not supported by any analytical justifications.…”

“…It is worth mentioning that other related papers also appeared in literature before ours [33], see, for example, Cinar [5] [43]. With our set objective, we shall revisit two recent studies (see [2] and [17]) and present more results regarding the topic discussed in these papers. In the first part of our paper, we consider the system of difference equations (Sys.…”

“…Perhaps because the result was not supported by any analytical justifications. Hence, in this work, we shall correct this mistake and offer some theoretical explanations on the results presented in [17]. The rest of the paper is organized as follows: in the next section (Section 2), we shall provide a theoretical explanation of Theorem 1, which can also be viewed as another way to prove the theorem.…”

“…Another recent work which shall be revisited here is due to Elsayed [17]. In [17], Elsayed investigated the behavior of solutions of several instances of the following system of nonlinear difference equations…”

“…In [17], Elsayed investigated the behavior of solutions of several instances of the following system of nonlinear difference equations…”