This monograph mainly divide into four categories, the first category has an introduction for some definitions, global asymptotic behavior, semi-cycle analysis, periodicity, convergence, bounded and unbounded solutions of second order nonlinear of power k difference equations and also higher order nonlinear difference equations; examples and survey for some papers which we generalize later. In the second and third part we introduce our new results which are considered as extensions and generalizations of some results on global asymptotic stability, oscillation, periodicity, semi-cycle analysis and boundedness of solutions of second order k-power non-linear difference equations. We introduce a definition of a k-power difference equation; also, in the second part we investigate the asymptotic behavior of solutions of difference equations and also in the third part we investigate the asymptotic behavior of solutions of difference equations. In the fourth part we present our new results which generalize the results of previous chapters, concerning third order rational recursive sequences to any odd order rational recursive sequences.

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