Multiplying the denominator and numerator of the right side by (1 + a) we obtainĪgarwal RP, Elsayed EM: On the solution of fourth-order rational recursive sequence. For some results in this area, for example: Agarwal and Elsayed studied the global stability, periodicity character and gave the solution form of some special cases of the recursive sequence Recently there has been a lot of interest in studying the global attractivity, boundedness character, periodicity and the solution form of nonlinear difference equations. Therefore, the study of rational difference equations of order greater than one is worth further consideration. However, there have not been any effective general methods to deal with the global behavior of rational difference equations of order greater than one so far. The study of rational difference equations of order greater than one is quite challenging and rewarding because some prototypes for the development of the basic theory of the global behavior of nonlinear difference equations of order greater than one come from the results for rational difference equations. Several results in the theory of difference equations have been obtained as more or less natural discrete analogues of corresponding results of differential equations. More importantly, difference equations also appear in the study of discretization methods for differential equations. Difference equations appear as natural descriptions of observed evolution phenomena because most measurements of time evolving variables are discrete and as such these equations are in their own right important mathematical models.
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